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666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
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⌀ | author
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
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| hash
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A383525 | a(n) = Sum_{k=0..floor(n/3)} binomial(n,k)^2 * binomial(n-2*k,k). | [
"1",
"1",
"1",
"10",
"33",
"76",
"370",
"1569",
"5089",
"20584",
"88776",
"336865",
"1336434",
"5639869",
"22824789",
"92230285",
"384930529",
"1595575648",
"6570596764",
"27418859721",
"114736740808",
"478594009281",
"2005907811469",
"8437974722463",
"35480386059826",
"149466347150701",
"631299305598625",
"2668522402478179"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A000172",
"A248658",
"A383525",
"A383526"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:56 | oeisdata/seq/A383/A383525.seq | 5fe97676253b44082a23765cc3302124 |
A383526 | a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k,k)^2. | [
"1",
"1",
"1",
"4",
"17",
"46",
"112",
"365",
"1297",
"4126",
"12686",
"41647",
"141440",
"470887",
"1553021",
"5205769",
"17665105",
"59858038",
"202599814",
"689183087",
"2355887902",
"8065291637",
"27637715887",
"94924591313",
"326810899744",
"1126888746871",
"3890420726167",
"13450563963085",
"46571447873597"
]
| [
"nonn"
]
| 7 | 0 | 4 | [
"A000172",
"A248658",
"A383525",
"A383526"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:52 | oeisdata/seq/A383/A383526.seq | caf0a708940da41e84f0c7803b7299ac |
A383527 | Partial sums of A005773. | [
"1",
"2",
"4",
"9",
"22",
"57",
"153",
"420",
"1170",
"3293",
"9339",
"26642",
"76363",
"219728",
"634312",
"1836229",
"5328346",
"15494125",
"45137995",
"131712826",
"384900937",
"1126265986",
"3299509114",
"9676690939",
"28407473191",
"83470059532",
"245465090758",
"722406781935",
"2127562036990",
"6270020029353"
]
| [
"nonn"
]
| 19 | 0 | 2 | [
"A000069",
"A001969",
"A002144",
"A002145",
"A005773",
"A005774",
"A005775",
"A010059",
"A097893",
"A122896",
"A167630",
"A210736",
"A211278",
"A257520",
"A383527"
]
| null | Mélika Tebni, Apr 29 2025 | 2025-05-10T13:17:13 | oeisdata/seq/A383/A383527.seq | 0345ee9e50598c3efd7f907729f90326 |
A383528 | a(n) = Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(n-2*k,k). | [
"1",
"1",
"1",
"5",
"11",
"19",
"57",
"149",
"325",
"841",
"2223",
"5387",
"13599",
"35435",
"89561",
"227397",
"587861",
"1508833",
"3865285",
"9980185",
"25767813",
"66439737",
"171835439",
"445009955",
"1152176511",
"2986869731",
"7752069847",
"20125928723",
"52286212535",
"135949102339",
"353648726393",
"920409996709"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A001850",
"A383528",
"A383529"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:02 | oeisdata/seq/A383/A383528.seq | 0b5319462478fb9362ed8bae46b2b628 |
A383529 | a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(n-3*k,k). | [
"1",
"1",
"1",
"1",
"6",
"13",
"22",
"33",
"91",
"226",
"474",
"877",
"1938",
"4586",
"10326",
"21409",
"45867",
"103423",
"234271",
"511426",
"1110544",
"2460822",
"5526188",
"12282861",
"27073156",
"59942598",
"133861825",
"298874122",
"664509858",
"1476912298",
"3294571470",
"7362783137",
"16437438777",
"36665641447",
"81881083752",
"183115618015"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A001850",
"A383528",
"A383529"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:06 | oeisdata/seq/A383/A383529.seq | 59577b3bca5902be40cc637c37d6eb88 |
A383530 | Number of non Wilf and non conjugate Wilf integer partitions of n. | [
"0",
"0",
"0",
"1",
"0",
"0",
"3",
"2",
"5",
"12",
"14",
"19",
"35",
"38",
"55",
"83",
"107",
"137",
"209",
"252",
"359",
"462",
"612",
"757",
"1032",
"1266",
"1649",
"2050",
"2617",
"3210",
"4111",
"4980",
"6262",
"7659",
"9479",
"11484",
"14224",
"17132",
"20962",
"25259",
"30693",
"36744",
"44517",
"53043",
"63850",
"75955",
"90943",
"107721",
"128485"
]
| [
"nonn"
]
| 8 | 0 | 7 | [
"A033461",
"A047966",
"A048767",
"A098859",
"A111133",
"A130091",
"A130092",
"A239455",
"A320348",
"A325324",
"A325325",
"A325349",
"A325351",
"A325367",
"A325368",
"A325388",
"A336866",
"A351293",
"A351294",
"A351295",
"A381431",
"A381432",
"A381433",
"A383506",
"A383507",
"A383512",
"A383513",
"A383530",
"A383531",
"A383532",
"A383534",
"A383709",
"A383712"
]
| null | Gus Wiseman, May 14 2025 | 2025-05-15T08:23:19 | oeisdata/seq/A383/A383530.seq | d0ec757d8129b49d6b3ab341d3031293 |
A383531 | Heinz numbers of integer partitions that do not have distinct multiplicities (Wilf) or distinct nonzero 0-appended differences (conjugate Wilf). | [
"6",
"21",
"30",
"36",
"42",
"60",
"65",
"66",
"70",
"78",
"84",
"90",
"102",
"105",
"110",
"114",
"120",
"126",
"132",
"133",
"138",
"140",
"150",
"154",
"156",
"165",
"168",
"174",
"180",
"186",
"198",
"204",
"210",
"216",
"220",
"222",
"228",
"231",
"234",
"238",
"240",
"246",
"252",
"258",
"264",
"270",
"273",
"276",
"280",
"282",
"286",
"294",
"300",
"306",
"308"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A001222",
"A001223",
"A047966",
"A048767",
"A055396",
"A056239",
"A061395",
"A098859",
"A112798",
"A122111",
"A130091",
"A130092",
"A181819",
"A238745",
"A320348",
"A325324",
"A325325",
"A325349",
"A325366",
"A325367",
"A325368",
"A325388",
"A336866",
"A351294",
"A351295",
"A381431",
"A383506",
"A383507",
"A383512",
"A383513",
"A383530",
"A383531",
"A383532",
"A383709",
"A383712"
]
| null | Gus Wiseman, May 15 2025 | 2025-05-16T18:50:51 | oeisdata/seq/A383/A383531.seq | e9ad5b141d19f2e89f60da667a474560 |
A383532 | Heinz numbers of integer partitions with distinct multiplicities (Wilf) and distinct nonzero 0-appended differences (conjugate Wilf). | [
"1",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"11",
"13",
"16",
"17",
"19",
"20",
"23",
"25",
"27",
"28",
"29",
"31",
"32",
"37",
"40",
"41",
"43",
"44",
"45",
"47",
"49",
"50",
"52",
"53",
"56",
"59",
"61",
"64",
"67",
"68",
"71",
"73",
"75",
"76",
"79",
"80",
"81",
"83",
"88",
"89",
"92",
"97",
"98",
"99",
"101",
"103",
"104",
"107",
"109",
"112",
"113",
"116",
"117",
"121",
"124",
"125"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A001222",
"A001223",
"A047966",
"A048767",
"A055396",
"A056239",
"A061395",
"A098859",
"A112798",
"A122111",
"A130091",
"A130092",
"A181819",
"A238745",
"A320348",
"A325324",
"A325325",
"A325349",
"A325366",
"A325367",
"A325368",
"A325388",
"A336866",
"A351294",
"A351295",
"A383506",
"A383507",
"A383512",
"A383513",
"A383530",
"A383531",
"A383532",
"A383709",
"A383712"
]
| null | Gus Wiseman, May 15 2025 | 2025-05-16T18:50:47 | oeisdata/seq/A383/A383532.seq | fbfd5d97116a115e857f624d5e6a3996 |
A383533 | Number of integer partitions of n with no ones such that it is possible to choose a family of pairwise disjoint strict integer partitions, one of each part. | [
"1",
"0",
"1",
"1",
"1",
"2",
"3",
"3",
"4",
"5",
"8",
"8",
"11",
"13",
"17",
"22",
"25",
"30",
"37",
"44",
"53",
"69",
"77",
"93",
"111",
"130",
"153",
"181",
"220",
"249",
"295"
]
| [
"nonn",
"more"
]
| 9 | 0 | 6 | [
"A044813",
"A047966",
"A048767",
"A048768",
"A089259",
"A098859",
"A116540",
"A130091",
"A217605",
"A239455",
"A242882",
"A317141",
"A318361",
"A351293",
"A351294",
"A351295",
"A381432",
"A381433",
"A381441",
"A381454",
"A382912",
"A382913",
"A383013",
"A383533",
"A383706",
"A383708",
"A383710",
"A383711"
]
| null | Gus Wiseman, May 07 2025 | 2025-05-08T22:57:03 | oeisdata/seq/A383/A383533.seq | 1f8bfc8212220dbe53fe54ffd5b6da67 |
A383534 | Irregular triangle read by rows where row n lists the positive first differences of the 0-prepended prime indices of n. | [
"1",
"2",
"1",
"3",
"1",
"1",
"4",
"1",
"2",
"1",
"2",
"5",
"1",
"1",
"6",
"1",
"3",
"2",
"1",
"1",
"7",
"1",
"1",
"8",
"1",
"2",
"2",
"2",
"1",
"4",
"9",
"1",
"1",
"3",
"1",
"5",
"2",
"1",
"3",
"10",
"1",
"1",
"1",
"11",
"1",
"2",
"3",
"1",
"6",
"3",
"1",
"1",
"1",
"12",
"1",
"7",
"2",
"4",
"1",
"2",
"13",
"1",
"1",
"2",
"14",
"1",
"4",
"2",
"1",
"1",
"8",
"15",
"1",
"1",
"4",
"1",
"2",
"2",
"5",
"1",
"5",
"16",
"1",
"1",
"3",
"2"
]
| [
"nonn",
"tabf"
]
| 7 | 1 | 2 | [
"A000040",
"A001221",
"A001222",
"A001223",
"A005117",
"A055396",
"A056239",
"A061395",
"A098859",
"A112798",
"A122111",
"A124010",
"A130091",
"A241919",
"A287352",
"A320348",
"A325324",
"A325325",
"A325349",
"A325366",
"A325367",
"A325368",
"A325388",
"A336866",
"A355536",
"A358137",
"A381431",
"A383506",
"A383512",
"A383513",
"A383534",
"A383535",
"A384008",
"A384009"
]
| null | Gus Wiseman, May 20 2025 | 2025-05-21T16:41:53 | oeisdata/seq/A383/A383534.seq | c8c46c02d80c63d335d7a240e05f8da7 |
A383535 | Heinz number of the positive first differences of the 0-prepended prime indices of n. | [
"1",
"2",
"3",
"2",
"5",
"4",
"7",
"2",
"3",
"6",
"11",
"4",
"13",
"10",
"6",
"2",
"17",
"4",
"19",
"6",
"9",
"14",
"23",
"4",
"5",
"22",
"3",
"10",
"29",
"8",
"31",
"2",
"15",
"26",
"10",
"4",
"37",
"34",
"21",
"6",
"41",
"12",
"43",
"14",
"6",
"38",
"47",
"4",
"7",
"6",
"33",
"22",
"53",
"4",
"15",
"10",
"39",
"46",
"59",
"8",
"61",
"58",
"9",
"2",
"25",
"20",
"67",
"26",
"51",
"12",
"71",
"4",
"73"
]
| [
"nonn"
]
| 6 | 1 | 2 | [
"A000040",
"A001222",
"A001223",
"A048767",
"A056239",
"A098859",
"A112798",
"A122111",
"A124010",
"A130091",
"A181819",
"A287352",
"A320348",
"A325324",
"A325351",
"A325366",
"A325367",
"A325368",
"A325388",
"A336866",
"A351294",
"A351295",
"A355536",
"A358137",
"A381431",
"A383512",
"A383513",
"A383534",
"A383535",
"A384008",
"A384009"
]
| null | Gus Wiseman, May 21 2025 | 2025-05-21T16:41:48 | oeisdata/seq/A383/A383535.seq | b390cb621db3d8f71f770822eb59d755 |
A383536 | a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,k)^2 * binomial(n-k,k). | [
"1",
"1",
"10",
"33",
"301",
"1468",
"12006",
"70945",
"548218",
"3588451",
"27033942",
"187329660",
"1398372925",
"10015968040",
"74666604910",
"545706810657",
"4076875022533",
"30186038308420",
"226302738440884",
"1690539173230083",
"12722171581599588",
"95650154853862786",
"722460110890588300"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A112019",
"A383536"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:48 | oeisdata/seq/A383/A383536.seq | 0f417e1ca65a9f936b3435676bf5e524 |
A383537 | a(n) = Sum_{k=0..floor(n/3)} binomial(n+k,k)^2 * binomial(n-2*k,k). | [
"1",
"1",
"1",
"17",
"51",
"109",
"981",
"4209",
"12637",
"79351",
"393493",
"1454021",
"7686459",
"39697057",
"166999101",
"823144689",
"4241896917",
"19293138685",
"93151760599",
"473739765167",
"2252548154403",
"10877558634801",
"54682637188009",
"266304982300197",
"1295171619802551",
"6466091747859771"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A383537",
"A383538"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:45 | oeisdata/seq/A383/A383537.seq | fd6731d8db003dcd874514b1bf629b07 |
A383538 | a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,k)^2 * binomial(n-3*k,k). | [
"1",
"1",
"1",
"1",
"26",
"73",
"148",
"257",
"2431",
"9676",
"26984",
"61993",
"332762",
"1487886",
"5029676",
"13986049",
"57394823",
"253491517",
"953613991",
"3032424076",
"11249004334",
"47032861778",
"185321607072",
"645015386921",
"2340940921276",
"9321743657318",
"37091865274327",
"136525692171310"
]
| [
"nonn"
]
| 9 | 0 | 5 | [
"A383536",
"A383537",
"A383538"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-04-29T08:54:26 | oeisdata/seq/A383/A383538.seq | bfcb2c86d69566c73d93c1a6cf288a36 |
A383539 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k)^2 * binomial(n-2*k,k). | [
"1",
"1",
"1",
"5",
"19",
"49",
"137",
"481",
"1645",
"5259",
"17309",
"59477",
"203931",
"693865",
"2384149",
"8277773",
"28797631",
"100312525",
"350891175",
"1232122535",
"4335809699",
"15287669469",
"54029225569",
"191351513905",
"678850904981",
"2412164275651",
"8584573648693",
"30595269827149"
]
| [
"nonn"
]
| 13 | 0 | 4 | [
"A098479",
"A383525",
"A383537",
"A383539"
]
| null | Seiichi Manyama, Apr 29 2025 | 2025-05-30T10:11:46 | oeisdata/seq/A383/A383539.seq | 7ff378478b2321e48d7898fcc6437946 |
A383540 | Positive numbers k such that (sin k)^k sets a new record. | [
"1",
"8",
"33",
"48269",
"48624",
"48979",
"49334",
"49689",
"50044",
"50399",
"50754",
"51109",
"51464",
"51819",
"52174",
"573204",
"37362253",
"42781604"
]
| [
"nonn",
"more"
]
| 13 | 1 | 2 | [
"A382815",
"A383540",
"A383541"
]
| null | Jwalin Bhatt, Apr 29 2025 | 2025-05-12T16:22:21 | oeisdata/seq/A383/A383540.seq | e597ca48522168b73822d1e18d3cdb7e |
A383541 | Positive numbers k such that (cos k)^k sets a new record. | [
"1",
"6",
"19",
"22",
"710",
"1146408",
"10838702",
"80143857",
"245850922",
"411557987",
"1068966896"
]
| [
"nonn",
"more"
]
| 27 | 1 | 2 | [
"A002485",
"A382564",
"A383540",
"A383541"
]
| null | Jwalin Bhatt, Apr 29 2025 | 2025-05-09T02:38:33 | oeisdata/seq/A383/A383541.seq | 3c05caa61aa9dd61517360fc650ec46c |
A383542 | a(n) = round(Shi(n)) where Shi(x) is the sinh integral function. | [
"0",
"1",
"3",
"5",
"10",
"20",
"43",
"96",
"220",
"519",
"1246",
"3036",
"7480",
"18599",
"46596",
"117478",
"297780",
"758319",
"1938952",
"4975454",
"12807826",
"33063593",
"85572336",
"221983185",
"577057696",
"1502975453",
"3921470496",
"10248248560",
"26822559296",
"70299597879",
"184486604704",
"484727787984"
]
| [
"nonn"
]
| 21 | 0 | 3 | [
"A383542",
"A383692"
]
| null | Kritsada Moomuang, May 05 2025 | 2025-05-10T23:00:16 | oeisdata/seq/A383/A383542.seq | c1c131c90538f6fde8507a0cc02f611e |
A383543 | a(n) is the largest number k such that i*n + 1 is squarefree for all 0 <= i <= k. | [
"2",
"3",
"0",
"1",
"2",
"3",
"0",
"0",
"2",
"7",
"0",
"1",
"1",
"6",
"0",
"2",
"0",
"15",
"0",
"3",
"2",
"1",
"0",
"0",
"2",
"0",
"0",
"5",
"2",
"3",
"0",
"6",
"2",
"4",
"0",
"7",
"1",
"3",
"0",
"1",
"2",
"3",
"0",
"0",
"2",
"7",
"0",
"0",
"0",
"6",
"0",
"4",
"0",
"5",
"0",
"2",
"2",
"1",
"0",
"1",
"2",
"0",
"0",
"7",
"2",
"7",
"0",
"6",
"2",
"4",
"0",
"3",
"1",
"0",
"0",
"1",
"2",
"7",
"0",
"0",
"2",
"6",
"0",
"1",
"1",
"6",
"0"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 1 | [
"A005117",
"A013929",
"A071808",
"A383543",
"A383544",
"A383545",
"A383546"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:03:37 | oeisdata/seq/A383/A383543.seq | 8d860a73a2a8adba928311d6360e16c8 |
A383544 | Numbers k such that A383543(k) > A383543(m) for all m < k. | [
"1",
"2",
"10",
"18",
"126",
"270",
"1470",
"1890",
"2310",
"7770",
"23100",
"28980",
"307230",
"325710",
"392700",
"1178100",
"1501500",
"2192190",
"3393390",
"10180170",
"19399380",
"29099070",
"38798760",
"310390080",
"1338557220",
"33910116240",
"601681470390",
"20056049013000",
"198755445718830",
"497390015522400",
"3579804188330370"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A071808",
"A383543",
"A383544",
"A383545",
"A383547"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:06:26 | oeisdata/seq/A383/A383544.seq | 77e179a2b564ac7cd04b2fcdcabcd47e |
A383545 | Record values in A383543. | [
"2",
"3",
"7",
"15",
"23",
"43",
"46",
"49",
"75",
"106",
"117",
"118",
"127",
"150",
"165",
"167",
"178",
"251",
"282",
"286",
"288",
"368",
"394",
"513",
"560",
"762",
"842",
"992",
"1154",
"1214",
"1264",
"1269",
"1313",
"1350",
"1376",
"1414",
"1471",
"1518",
"1592",
"1816",
"1851",
"1940",
"1946",
"2017",
"2101",
"2117",
"2122",
"2159",
"2191",
"2244",
"2393"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A071808",
"A383543",
"A383544",
"A383545",
"A383548"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:04:49 | oeisdata/seq/A383/A383545.seq | 0ef696cd58efbd085e4685db8c1c8066 |
A383546 | a(n) is the largest number k such that i*n - 1 is squarefree for all 1 <= i <= k, or 0 if no such number exists. | [
"0",
"4",
"2",
"6",
"0",
"20",
"2",
"7",
"0",
"0",
"2",
"22",
"0",
"1",
"2",
"3",
"0",
"6",
"0",
"4",
"0",
"6",
"1",
"23",
"0",
"0",
"2",
"0",
"0",
"17",
"2",
"1",
"0",
"3",
"2",
"14",
"0",
"1",
"2",
"6",
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"2",
"2",
"3",
"0",
"0",
"2",
"11",
"0",
"0",
"0",
"3",
"0",
"9",
"0",
"4",
"0",
"4",
"1",
"8",
"0",
"7",
"1",
"0",
"0",
"10",
"2",
"1",
"0",
"3",
"2",
"7",
"0",
"1",
"2",
"0",
"0",
"16",
"2",
"7",
"0",
"0",
"2",
"13",
"0"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 2 | [
"A005117",
"A013929",
"A071809",
"A383543",
"A383546",
"A383547",
"A383548"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:05:22 | oeisdata/seq/A383/A383546.seq | dcd8d4c4e160384338f94cb5d5ceab53 |
A383547 | Numbers k such that A383546(k) > A383546(m) for all m < k. | [
"1",
"2",
"4",
"6",
"12",
"24",
"120",
"150",
"240",
"300",
"840",
"1680",
"2730",
"6090",
"32340",
"106260",
"145530",
"154770",
"1554630",
"1861860",
"2072070",
"2642640",
"5105100",
"28918890",
"77507430",
"99549450",
"717777060",
"3714981270",
"5577321750",
"6692786100",
"95929934100",
"188736568020",
"512444322390",
"1348596399150"
]
| [
"nonn"
]
| 12 | 1 | 2 | [
"A071809",
"A383544",
"A383546",
"A383547",
"A383548"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:06:10 | oeisdata/seq/A383/A383547.seq | 4091c77dcac2163394dba2708b9a6eef |
A383548 | Record values in A383546. | [
"0",
"4",
"6",
"20",
"22",
"23",
"28",
"32",
"38",
"39",
"68",
"94",
"104",
"117",
"129",
"135",
"151",
"163",
"167",
"213",
"235",
"270",
"275",
"277",
"283",
"356",
"416",
"445",
"453",
"533",
"586",
"639",
"784",
"803",
"836",
"1073",
"1223",
"1252",
"1313",
"1314",
"1508",
"1549",
"1558",
"1559",
"1599",
"1605",
"1631",
"1644",
"1676",
"1692",
"1694",
"1738",
"1834"
]
| [
"nonn"
]
| 12 | 1 | 2 | [
"A071808",
"A383545",
"A383546",
"A383547",
"A383548"
]
| null | Amiram Eldar, Apr 30 2025 | 2025-05-04T02:05:51 | oeisdata/seq/A383/A383548.seq | dd6716ae7e069be50fee606bbb5dd743 |
A383549 | Number of rises in all compositions of n with parts in {1,2,3} and adjacent differences in {-1,1}. | [
"0",
"0",
"0",
"1",
"1",
"2",
"5",
"3",
"9",
"11",
"10",
"24",
"21",
"30",
"50",
"43",
"75",
"93",
"96",
"161",
"170",
"215",
"312",
"323",
"456",
"574",
"639",
"906",
"1046",
"1276",
"1710",
"1935",
"2501",
"3135",
"3642",
"4760",
"5699",
"6893",
"8823",
"10401",
"12952",
"16079",
"19104",
"24002",
"29097",
"35165",
"43865",
"52628",
"64503",
"79363",
"95329"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 6 | [
"A011782",
"A076118",
"A124760",
"A151842",
"A173258",
"A214247",
"A220062",
"A238343",
"A383549"
]
| null | John Tyler Rascoe, Apr 29 2025 | 2025-05-04T03:21:30 | oeisdata/seq/A383/A383549.seq | c6e86c1ec39ef499c9160f495108defd |
A383550 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (2,0),(0,2),(3,3). | [
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"3",
"1",
"3",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"4",
"2",
"6",
"2",
"4",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"5",
"3",
"10",
"6",
"10",
"3",
"5",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"6",
"4",
"15",
"12",
"21",
"12",
"15",
"4",
"6",
"0",
"1"
]
| [
"nonn",
"tabl"
]
| 12 | 0 | 13 | [
"A027907",
"A053442",
"A383550",
"A383567"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:14:11 | oeisdata/seq/A383/A383550.seq | cfa19bde065d3378db48ec1755ec70bf |
A383551 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(0,1),(3,3). | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"6",
"4",
"1",
"1",
"5",
"10",
"10",
"5",
"1",
"1",
"6",
"15",
"21",
"15",
"6",
"1",
"1",
"7",
"21",
"37",
"37",
"21",
"7",
"1",
"1",
"8",
"28",
"59",
"76",
"59",
"28",
"8",
"1",
"1",
"9",
"36",
"88",
"138",
"138",
"88",
"36",
"9",
"1",
"1",
"10",
"45",
"125",
"230",
"282",
"230",
"125",
"45",
"10",
"1",
"1",
"11",
"55",
"171",
"360",
"522",
"522",
"360",
"171",
"55",
"11",
"1"
]
| [
"nonn",
"tabl"
]
| 9 | 0 | 5 | [
"A376791",
"A383551"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:13:48 | oeisdata/seq/A383/A383551.seq | 3d2d077b68a2436feaee8aa15232eef4 |
A383552 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(0,1),(2,2). | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"7",
"4",
"1",
"1",
"5",
"12",
"12",
"5",
"1",
"1",
"6",
"18",
"26",
"18",
"6",
"1",
"1",
"7",
"25",
"47",
"47",
"25",
"7",
"1",
"1",
"8",
"33",
"76",
"101",
"76",
"33",
"8",
"1",
"1",
"9",
"42",
"114",
"189",
"189",
"114",
"42",
"9",
"1",
"1",
"10",
"52",
"162",
"321",
"404",
"321",
"162",
"52",
"10",
"1",
"1",
"11",
"63",
"221",
"508",
"772",
"772",
"508",
"221",
"63",
"11",
"1"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 5 | [
"A008288",
"A349713",
"A383551",
"A383552",
"A383566"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:11:40 | oeisdata/seq/A383/A383552.seq | 52a3732f56b651c25bd38805b0ffcbe3 |
A383553 | G.f. A(x) satisfies A( x*(1 - x*A(x)) )^2 = A(x) / (1 - x*A(x)). | [
"1",
"1",
"4",
"25",
"203",
"1986",
"22492",
"287779",
"4092708",
"63950627",
"1088344063",
"20034723586",
"396685773847",
"8407897764860",
"189983677908848",
"4559916912174055",
"115878339541378537",
"3108738814550013980",
"87811656459134922064",
"2605292980183085241385",
"81009590895282761666579",
"2634565319518560418484917"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A383553",
"A383554",
"A383555"
]
| null | Paul D. Hanna, Apr 30 2025 | 2025-06-09T05:22:05 | oeisdata/seq/A383/A383553.seq | 70e9d27b44e6d7d7dedd3e6e47e9a3f2 |
A383554 | G.f. B(x) satisfies B(x)^2 = B(x*B(x)) / (1 - x*B(x)). | [
"1",
"1",
"3",
"15",
"106",
"960",
"10458",
"131608",
"1864069",
"29203507",
"499950326",
"9270102872",
"184914799822",
"3946947403992",
"89751996370928",
"2166232174120558",
"55315057188777104",
"1490116322734948876",
"42239882837124257362",
"1257015386867813340506",
"39187639539046005580139",
"1277312296443107349977421"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A383553",
"A383554",
"A383555"
]
| null | Paul D. Hanna, May 03 2025 | 2025-06-09T05:22:39 | oeisdata/seq/A383/A383554.seq | 90ea115821df3a3293330ca38db18249 |
A383555 | G.f. C(x) satisfies C(x) = (1 - x/C(x)) * C(x/C(x))^2. | [
"1",
"1",
"2",
"8",
"53",
"474",
"5160",
"65044",
"923050",
"14485824",
"248342433",
"4610040310",
"92042354800",
"1966041657574",
"44732916501187",
"1080164746159166",
"27592519521492907",
"743533900115940394",
"21082015219948566983",
"627509220974664243742",
"19566084047915645708631",
"637845348518456030195620"
]
| [
"nonn"
]
| 19 | 0 | 3 | [
"A383553",
"A383554",
"A383555"
]
| null | Paul D. Hanna, May 03 2025 | 2025-06-09T05:21:27 | oeisdata/seq/A383/A383555.seq | 1209dc46d932b777cf137f4ea06a6fef |
A383556 | G.f. A(x) satisfies [x^n] A(x)^n = [x^n] -1/A(x)^(n+1) for n > 1 with A(0) = 1, A'(0) = 1. | [
"1",
"1",
"7",
"163",
"7295",
"497193",
"46629734",
"5701678075",
"878881320340",
"166768493380169",
"38240722520600933",
"10435986606153478637",
"3345526178030524399987",
"1245613832452691368917233",
"533281483558996002057816770",
"260228921614773660248756394778",
"143609349303434423698940591120719"
]
| [
"nonn"
]
| 11 | 0 | 3 | null | null | Paul D. Hanna, May 17 2025 | 2025-05-18T03:19:27 | oeisdata/seq/A383/A383556.seq | 3ac741450ef27ae7393e3ba9437a9f85 |
A383557 | G.f. A(x) satisfies: Sum_{n>=0} x^n * A(x)^(n*(n-1)) = 1/Sum_{n>=0} (-1)^n * x^n * A(x)^(n^2). | [
"1",
"1",
"5",
"31",
"219",
"1694",
"13994",
"121410",
"1093480",
"10141721",
"96319038",
"932974034",
"9189767159",
"91843859618",
"929737369160",
"9520350467469",
"98508339702499",
"1029120790761273",
"10848277404444721",
"115332595879627333",
"1236215234785069596",
"13356483685654097089",
"145444925937547162484",
"1596284433654881047888"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A337913",
"A383557",
"A383558"
]
| null | Paul D. Hanna, Jun 04 2025 | 2025-06-05T09:56:09 | oeisdata/seq/A383/A383557.seq | 91f9eb02fa79087f77bae0c605996cd7 |
A383558 | G.f. A(x) satisfies: Sum_{n>=0} x^n * A(x)^(n^2) = 1/Sum_{n>=0} (-1)^n * x^n * A(x)^(n*(n+1)). | [
"1",
"1",
"6",
"47",
"424",
"4175",
"43617",
"475457",
"5350757",
"61727826",
"726360262",
"8686960066",
"105308656277",
"1291367772947",
"15992962919905",
"199777529838694",
"2514520265005606",
"31863092830768302",
"406201872497094718",
"5206720221580284591",
"67072172226855680831",
"867953975985508272626",
"11279109566312519301208"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A337913",
"A383557",
"A383558"
]
| null | Paul D. Hanna, Jun 04 2025 | 2025-06-05T09:56:12 | oeisdata/seq/A383/A383558.seq | 1ca541de04ea2c5ef0252c8335017c79 |
A383559 | O.g.f. A(x) satisfies: [x^n] exp( n*(2*n+1)*x ) / A(x) = 0 for n > 0. | [
"1",
"3",
"29",
"609",
"20857",
"997671",
"61114409",
"4548317073",
"397323349505",
"39774233809179",
"4483232458612245",
"561425116837715457",
"77289022946177141161",
"11597365849594347661839",
"1883429636306366952452433",
"329083700898584984268782241",
"61549497773760817234065857793",
"12268604214374346472111552473267"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A304319",
"A337458",
"A383559"
]
| null | Paul D. Hanna, May 17 2025 | 2025-05-24T03:06:05 | oeisdata/seq/A383/A383559.seq | ed1b9b6edb2e5c92c820e446c0c52a49 |
A383560 | E.g.f. satisfies A(x) = exp(-x*A(x)) * A( x*exp(-x*A(x)) )^2. | [
"1",
"1",
"7",
"118",
"3517",
"160086",
"10224319",
"867305622",
"94034404377",
"12665879397046",
"2073375227292691",
"405303998554127718",
"93253207746857953381",
"24948396475041099571590",
"7680545481780577676806215",
"2696379400609033981226573206",
"1070917017856110681841654586929",
"477809258637756188291409832547094"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A383560",
"A383561",
"A383562"
]
| null | Paul D. Hanna, May 01 2025 | 2025-05-03T09:35:13 | oeisdata/seq/A383/A383560.seq | c7456f7f79295face8443b29dee08c74 |
A383561 | E.g.f. B(x) satisfies B(x)^2 = exp(x*B(x)) * B(x*B(x)). | [
"1",
"1",
"5",
"67",
"1761",
"75291",
"4676833",
"393156443",
"42661238049",
"5778857710603",
"953295948777201",
"187879651901314011",
"43567356033945471313",
"11738730471967494152795",
"3636438743736060718972545",
"1283505233869526097965732971",
"512110262770880950252243273281",
"229380028602428037581395066474347"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A383560",
"A383561",
"A383562"
]
| null | Paul D. Hanna, May 01 2025 | 2025-05-03T09:35:09 | oeisdata/seq/A383/A383561.seq | 626a6f791eed00f27280d0f872597f55 |
A383562 | E.g.f. C(x) satisfies C(x) = exp(-x/C(x)) * C(x/C(x))^2. | [
"1",
"1",
"3",
"34",
"869",
"37046",
"2305267",
"194264862",
"21126164649",
"2866926282454",
"473618723892911",
"93448926633746366",
"21689210323474282525",
"5848029460632243552630",
"1812621760896079629017355",
"640062219045088105574834686",
"255472389087185984365656473681",
"114462401664425227281876155867990"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A383560",
"A383561",
"A383562"
]
| null | Paul D. Hanna, May 01 2025 | 2025-05-03T09:35:05 | oeisdata/seq/A383/A383562.seq | d0a7b134fcbda9ec1033bbffb1cc5689 |
A383563 | G.f. A(x) satisfies A( x*(1+x)/A(x)^2 ) = 1 + x. | [
"1",
"1",
"1",
"3",
"13",
"72",
"465",
"3362",
"26531",
"224856",
"2024188",
"19202830",
"190857879",
"1978567663",
"21319434418",
"238109360460",
"2750229390071",
"32789591062124",
"402891169846242",
"5094855923807780",
"66229610059651788",
"884081025776797026",
"12107164229698851942",
"169954380180177899277",
"2443554376412586234247"
]
| [
"nonn"
]
| 18 | 0 | 4 | [
"A121687",
"A145345",
"A383563",
"A384265"
]
| null | Paul D. Hanna, May 26 2025 | 2025-06-01T19:39:39 | oeisdata/seq/A383/A383563.seq | f1498664bf4226bce245bd7b3c6a2d7a |
A383564 | G.f. A(x) satisfies 1 = Sum{n=-oo..+oo} (x^n - 2*x*A(x)^n)^n. | [
"1",
"2",
"11",
"63",
"313",
"953",
"-2103",
"-52455",
"-340989",
"-684583",
"3097817",
"-42019812",
"-959576394",
"2335125550",
"229613772815",
"2356225506958",
"-11899498155741",
"-527484556204563",
"-3363552193233237",
"67551575645570526",
"1470281680830417628",
"2115661347716495378",
"-323942681936663419906",
"-4680631899371554723607",
"23014994879777225773481"
]
| [
"sign"
]
| 7 | 0 | 2 | [
"A383564",
"A383565"
]
| null | Paul D. Hanna, May 21 2025 | 2025-05-21T10:42:55 | oeisdata/seq/A383/A383564.seq | efcf57ca26cbb2fd9886d0670c8c22fa |
A383565 | G.f. A(x) satisfies 1 = Sum{n=-oo..+oo} (2*x*A(x)^(n-2) - x^n)^n. | [
"1",
"2",
"5",
"51",
"420",
"4281",
"46511",
"545096",
"6692705",
"85823095",
"1139652239",
"15617770854",
"220169697660",
"3186889572660",
"47301102618948",
"719343250099901",
"11204504778316013",
"178732002565811126",
"2920246793283514209",
"48883298337473391637",
"838635194555095619608",
"14750589639992176103092",
"266072885796042137133800"
]
| [
"nonn"
]
| 7 | 0 | 2 | null | null | Paul D. Hanna, May 21 2025 | 2025-05-21T10:44:49 | oeisdata/seq/A383/A383565.seq | 735d407010fef21059570809e85a28f8 |
A383566 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(0,1),(4,4). | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"6",
"4",
"1",
"1",
"5",
"10",
"10",
"5",
"1",
"1",
"6",
"15",
"20",
"15",
"6",
"1",
"1",
"7",
"21",
"35",
"35",
"21",
"7",
"1",
"1",
"8",
"28",
"56",
"71",
"56",
"28",
"8",
"1",
"1",
"9",
"36",
"84",
"128",
"128",
"84",
"36",
"9",
"1",
"1",
"10",
"45",
"120",
"213",
"258",
"213",
"120",
"45",
"10",
"1",
"1",
"11",
"55",
"165",
"334",
"474",
"474",
"334",
"165",
"55",
"11",
"1"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 5 | [
"A008288",
"A376792",
"A383551",
"A383552",
"A383566"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:12:30 | oeisdata/seq/A383/A383566.seq | 43eddb0fb5fd0e5a979ca4dbc6d3c04e |
A383567 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (2,0),(0,2),(5,5). | [
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"3",
"0",
"3",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"4",
"0",
"6",
"0",
"4",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"5",
"0",
"10",
"1",
"10",
"0",
"5",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"6",
"0",
"15",
"2",
"20",
"2",
"15",
"0",
"6",
"0",
"1"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 13 | [
"A027907",
"A383550",
"A383567",
"A383568"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:14:06 | oeisdata/seq/A383/A383567.seq | f0c7f93f518cdffa896c10181b205358 |
A383568 | Expansion of 1/sqrt((1-x^5)^2 - 4*x^2). | [
"1",
"0",
"2",
"0",
"6",
"1",
"20",
"6",
"70",
"30",
"253",
"140",
"936",
"630",
"3522",
"2773",
"13430",
"12032",
"51770",
"51690",
"201389",
"220470",
"789546",
"935330",
"3116416",
"3951949",
"12373910",
"16645398",
"49389050",
"69938416",
"198048409",
"293296470",
"797461358",
"1228136090",
"3222960100",
"5136602753"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A002426",
"A053442",
"A383567",
"A383568",
"A383569"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:13:57 | oeisdata/seq/A383/A383568.seq | d5a115165b13876c624173c90e5152be |
A383569 | Expansion of 1/sqrt((1-x^7)^2 - 4*x^2). | [
"1",
"0",
"2",
"0",
"6",
"0",
"20",
"1",
"70",
"6",
"252",
"30",
"924",
"140",
"3433",
"630",
"12882",
"2772",
"48710",
"12012",
"185316",
"51481",
"708582",
"218810",
"2720788",
"923990",
"10484684",
"3881556",
"40528441",
"16236486",
"157086660",
"67675972",
"610318610",
"281236620",
"2376289056",
"1165715161",
"9269869182"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A002426",
"A053442",
"A383568",
"A383569"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:13:53 | oeisdata/seq/A383/A383569.seq | 20da64754fa8202b73c80d727df06620 |
A383571 | Expansion of 1/sqrt((1-x^3)^2 - 4*x^4). | [
"1",
"0",
"0",
"1",
"2",
"0",
"1",
"6",
"6",
"1",
"12",
"30",
"21",
"20",
"90",
"141",
"100",
"210",
"561",
"672",
"672",
"1681",
"3206",
"3528",
"5125",
"11622",
"17892",
"21253",
"38172",
"74052",
"102565",
"141680",
"268092",
"454741",
"622182",
"979836",
"1790361",
"2784366",
"3993132",
"6741593",
"11587758",
"17380116",
"26551097",
"45489082",
"74098518"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A002426",
"A053442",
"A182883",
"A376791",
"A383571",
"A383572"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:11:37 | oeisdata/seq/A383/A383571.seq | 8958c9b7a3463f04c01d849188e02abe |
A383572 | Expansion of 1/sqrt((1-x^4)^2 - 4*x^5). | [
"1",
"0",
"0",
"0",
"1",
"2",
"0",
"0",
"1",
"6",
"6",
"0",
"1",
"12",
"30",
"20",
"1",
"20",
"90",
"140",
"71",
"30",
"210",
"560",
"631",
"294",
"420",
"1680",
"3151",
"2828",
"1680",
"4200",
"11551",
"16704",
"13272",
"12672",
"34651",
"72162",
"86064",
"69960",
"102961",
"252362",
"423390",
"446160",
"429001",
"805508",
"1685970",
"2393820",
"2419561"
]
| [
"nonn"
]
| 9 | 0 | 6 | [
"A002426",
"A182883",
"A376792",
"A383571",
"A383572"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:11:32 | oeisdata/seq/A383/A383572.seq | eb4662251b505cf334363d17a16a4421 |
A383573 | a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(2*(n-2*k),n-2*k). | [
"1",
"2",
"7",
"24",
"89",
"338",
"1311",
"5152",
"20449",
"81778",
"328999",
"1330008",
"5398265",
"21984610",
"89791103",
"367643776",
"1508560257",
"6201927074",
"25540266503",
"105336838616",
"435035342553",
"1798875915826",
"7446653956895",
"30857577536800",
"127987031688161",
"531301328367762",
"2207281722474919"
]
| [
"nonn"
]
| 23 | 0 | 2 | [
"A026375",
"A360290",
"A383573",
"A383581",
"A383582"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-05-03T22:26:07 | oeisdata/seq/A383/A383573.seq | c7e70612d3055a563c7db6f4fef96990 |
A383574 | Fourth column of A353077. | [
"9",
"14",
"8",
"-1",
"13",
"7",
"9",
"-1",
"12",
"-1",
"16",
"-1",
"-1",
"7",
"21",
"-1",
"12",
"-1",
"-1",
"-1",
"13",
"-1",
"33",
"-1",
"9",
"-1",
"12",
"-1",
"13",
"7",
"-1",
"-1",
"-1",
"-1",
"19",
"-1",
"-1",
"-1",
"8",
"-1",
"10",
"-1",
"-1",
"-1",
"10",
"-1",
"25",
"-1",
"-1",
"-1",
"15",
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"-1",
"-1",
"-1",
"8",
"-1",
"16",
"-1",
"-1",
"7",
"-1",
"-1",
"12",
"-1",
"-1"
]
| [
"sign"
]
| 55 | 4 | 1 | [
"A000961",
"A333852",
"A353077",
"A373514",
"A383574"
]
| null | Martin Becker, May 03 2025 | 2025-05-24T10:36:05 | oeisdata/seq/A383/A383574.seq | 3960ab300582b3182a987e7901d424c5 |
A383575 | Characteristic function of numbers of the form k = m^e, where m is squarefree and (-1)^omega(k) = mu(e). | [
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
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"1",
"0",
"0",
"1",
"1"
]
| [
"nonn"
]
| 20 | 1 | null | [
"A001221",
"A005117",
"A008683",
"A382883",
"A383016",
"A383575",
"A383576",
"A384667",
"A385055"
]
| null | Friedjof Tellkamp, Jun 14 2025 | 2025-06-17T02:57:28 | oeisdata/seq/A383/A383575.seq | dc43d927bb2d719d20014b6205b4b3a8 |
A383576 | Characteristic function of numbers of the form k = m^e, where m is squarefree and (-1)^omega(k) = -mu(e). | [
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
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"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0"
]
| [
"nonn"
]
| 19 | 1 | null | [
"A001221",
"A005117",
"A008683",
"A382883",
"A383017",
"A383575",
"A383576",
"A384667",
"A384709"
]
| null | Friedjof Tellkamp, Jun 14 2025 | 2025-06-17T02:57:32 | oeisdata/seq/A383/A383576.seq | e3a723cc17a47c374c600727a1d9cc0f |
A383577 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k) * binomial(n-2*k,k)^2. | [
"1",
"1",
"1",
"3",
"13",
"37",
"87",
"241",
"793",
"2513",
"7437",
"22287",
"70051",
"222883",
"700213",
"2195139",
"6959869",
"22252933",
"71201129",
"227826699",
"731309001",
"2356460041",
"7609531843",
"24603325189",
"79677148959",
"258535824775",
"840291483835",
"2734637778217",
"8910389207081",
"29069537051081"
]
| [
"nonn"
]
| 7 | 0 | 4 | [
"A383539",
"A383577"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-04-30T09:11:23 | oeisdata/seq/A383/A383577.seq | ee9c7e0b93587563140457be7d051371 |
A383578 | Let p = prime(n), then a(n) is the p-smooth part of (p-1)!+1. | [
"2",
"3",
"25",
"7",
"11",
"169",
"17",
"19",
"23",
"29",
"31",
"37",
"41",
"43",
"47",
"53",
"59",
"61",
"67",
"71",
"73",
"79",
"83",
"89",
"97",
"101",
"103",
"107",
"109",
"113",
"127",
"131",
"137",
"139",
"149",
"151",
"157",
"163",
"167",
"173",
"179",
"181",
"191",
"193",
"197",
"199",
"211",
"223",
"227",
"229",
"233",
"239",
"241",
"251",
"257",
"263",
"269",
"271",
"277",
"281",
"283",
"293"
]
| [
"nonn"
]
| 29 | 1 | 1 | [
"A007540",
"A060371",
"A383257",
"A383578"
]
| null | Mike Jones, Apr 30 2025 | 2025-05-15T08:24:13 | oeisdata/seq/A383/A383578.seq | ef9bdcae4cd61fa57509e427c05798e3 |
A383579 | a(n) is the largest number t such that there exist numbers i,j,k such that, for all m <= t, there exist integers x,y,z with x*i + y*j + z*k = m and |x|+|y|+|z| <= n. | [
"0",
"3",
"10",
"24",
"46",
"80",
"129",
"196",
"277",
"372",
"500",
"660",
"842",
"1046",
"1272",
"1560",
"1883",
"2236",
"2619",
"3040",
"3544",
"4086",
"4666",
"5284",
"5969",
"6740",
"7557",
"8420",
"9329",
"10342",
"11436",
"12584",
"13786",
"15042",
"16447",
"17920",
"19455",
"21052",
"22734",
"24572",
"26480",
"28458",
"30506",
"32684",
"35005",
"37404"
]
| [
"nonn"
]
| 28 | 0 | 2 | [
"A002378",
"A383579"
]
| null | Zachary Barbanell, Apr 30 2025 | 2025-05-14T06:46:23 | oeisdata/seq/A383/A383579.seq | 8eb3374f84ae95800ce454ce24bdb424 |
A383580 | a(n) is the largest number t such that there exist numbers i,j,k,l such that, for all m <= t, there exist integers x,y,z,w with x*i + y*j + z*k + w*l = m and |x|+|y|+|z|+|w| <= n. | [
"0",
"4",
"16",
"47",
"104",
"207",
"375",
"624",
"984",
"1475"
]
| [
"nonn",
"more"
]
| 4 | 0 | 2 | [
"A002378",
"A383579",
"A383580"
]
| null | Zachary Barbanell, May 14 2025 | 2025-05-19T22:17:52 | oeisdata/seq/A383/A383580.seq | bf7f5d3d4a1e0970188db382b4bb0547 |
A383581 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-3*k),n-3*k). | [
"1",
"2",
"6",
"21",
"74",
"270",
"1005",
"3788",
"14418",
"55289",
"213270",
"826614",
"3216629",
"12558928",
"49175136",
"193023965",
"759299438",
"2992534344",
"11813985377",
"46709675040",
"184928644350",
"733047010709",
"2908981549006",
"11555513379450",
"45945148281437",
"182835149061920",
"728149606630164"
]
| [
"nonn"
]
| 16 | 0 | 2 | [
"A026375",
"A360291",
"A376791",
"A383571",
"A383573",
"A383581",
"A383582"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-05-02T08:00:38 | oeisdata/seq/A383/A383581.seq | 0e1d51c097a1908e0bb411e879e37403 |
A383582 | a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*(n-4*k),n-4*k). | [
"1",
"2",
"6",
"20",
"71",
"256",
"942",
"3512",
"13221",
"50138",
"191260",
"733088",
"2821037",
"10892100",
"42174848",
"163706656",
"636816019",
"2481902842",
"9689155902",
"37882580356",
"148313102097",
"581365577564",
"2281393560802",
"8961689897248",
"35235582858441",
"138657185501870",
"546064549476476"
]
| [
"nonn"
]
| 24 | 0 | 2 | [
"A026375",
"A360292",
"A376792",
"A383572",
"A383573",
"A383581",
"A383582"
]
| null | Seiichi Manyama, Apr 30 2025 | 2025-05-03T09:40:48 | oeisdata/seq/A383/A383582.seq | de15e7b78d62f5b38ed0ef914f3a1d34 |
A383583 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(k,n-3*k). | [
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"3",
"0",
"3",
"12",
"10",
"4",
"30",
"60",
"40",
"60",
"210",
"286",
"231",
"560",
"1267",
"1428",
"1722",
"4208",
"7182",
"8064",
"13275",
"28080",
"40656",
"51754",
"97020",
"176088",
"240251",
"355872",
"667810",
"1081092",
"1506648",
"2475616",
"4401696",
"6693492",
"9904752",
"16950662",
"28359201"
]
| [
"nonn"
]
| 16 | 0 | 8 | [
"A005717",
"A383571",
"A383583",
"A383584"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-03T14:22:14 | oeisdata/seq/A383/A383583.seq | 377d77cad204e521ea4f681732d50e66 |
A383584 | a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(k,n-4*k). | [
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"3",
"0",
"0",
"3",
"12",
"10",
"0",
"4",
"30",
"60",
"35",
"5",
"60",
"210",
"280",
"132",
"105",
"560",
"1260",
"1267",
"630",
"1260",
"4200",
"6938",
"5796",
"4236",
"11550",
"27729",
"36396",
"28644",
"34155",
"90100",
"168663",
"188100",
"163020",
"276573",
"631290",
"973830",
"995280",
"1068222",
"2111252",
"4104100"
]
| [
"nonn"
]
| 16 | 0 | 10 | [
"A005717",
"A383572",
"A383583",
"A383584"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-02T03:18:18 | oeisdata/seq/A383/A383584.seq | 9e4cfd8abd09fc9b6fd9a3abfacceaa8 |
A383585 | Number of vertices of even degree in a cubic lattice n X n X n. | [
"0",
"0",
"13",
"32",
"63",
"112",
"185",
"288",
"427",
"608",
"837",
"1120",
"1463",
"1872",
"2353",
"2912",
"3555",
"4288",
"5117",
"6048",
"7087",
"8240",
"9513",
"10912",
"12443",
"14112",
"15925",
"17888",
"20007",
"22288",
"24737",
"27360",
"30163",
"33152",
"36333",
"39712",
"43295",
"47088",
"51097",
"55328",
"59787",
"64480",
"69413",
"74592",
"80023",
"85712",
"91665",
"97888"
]
| [
"nonn",
"easy"
]
| 31 | 1 | 3 | [
"A000578",
"A383585"
]
| null | Nicolay Avilov, May 01 2025 | 2025-05-19T11:42:05 | oeisdata/seq/A383/A383585.seq | dcabbe553b88147e50799badc63a643c |
A383586 | a(n) is the minimum sum of a nonnegative integer 4-tuple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller. | [
"0",
"4",
"10",
"20",
"40",
"76",
"177",
"387",
"829",
"1749"
]
| [
"nonn",
"more"
]
| 16 | 0 | 2 | [
"A256001",
"A383586",
"A383587",
"A383588"
]
| null | Gerold Jager, May 01 2025 | 2025-05-08T05:01:36 | oeisdata/seq/A383/A383586.seq | 3c74035cb1acc11090449690764f6b51 |
A383587 | a(n) is the minimum sum of a nonnegative integer 5-tuple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller. | [
"0",
"5",
"15",
"31",
"71",
"176",
"444"
]
| [
"nonn",
"more"
]
| 17 | 0 | 2 | [
"A256001",
"A383586",
"A383587",
"A383588"
]
| null | Gerold Jager, May 01 2025 | 2025-05-12T19:42:39 | oeisdata/seq/A383/A383587.seq | 7502c42c4600880a0daffe24602b9782 |
A383588 | a(n) is the minimum sum of a nonnegative integer 6-tuple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller. | [
"0",
"6",
"21",
"45",
"123",
"335"
]
| [
"nonn",
"more"
]
| 14 | 0 | 2 | [
"A256001",
"A383586",
"A383587",
"A383588"
]
| null | Gerold Jager, May 01 2025 | 2025-05-12T19:27:33 | oeisdata/seq/A383/A383588.seq | a13a5b0e13515474a3bb1592d6febac2 |
A383589 | a(n) = A378762(A381662(n)). | [
"1",
"2",
"3",
"6",
"5",
"4",
"7",
"10",
"9",
"8",
"15",
"12",
"13",
"14",
"11",
"16",
"21",
"18",
"19",
"20",
"17",
"28",
"23",
"26",
"25",
"24",
"27",
"22",
"29",
"36",
"31",
"34",
"33",
"32",
"35",
"30",
"45",
"38",
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"40",
"41",
"42",
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"44",
"37",
"46",
"55",
"48",
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"50",
"51",
"52",
"49",
"54",
"47",
"66",
"57",
"64",
"59",
"62",
"61",
"60",
"63",
"58",
"65",
"56"
]
| [
"nonn",
"tabf"
]
| 11 | 1 | 2 | [
"A000027",
"A000384",
"A016813",
"A376214",
"A378684",
"A379342",
"A379343",
"A380200",
"A380245",
"A380815",
"A380817",
"A381662",
"A381663",
"A381664",
"A381968",
"A382499",
"A382679",
"A382680",
"A383589"
]
| null | Boris Putievskiy, May 01 2025 | 2025-05-06T11:24:05 | oeisdata/seq/A383/A383589.seq | 133e0a5fea673cd5da95679251e1948b |
A383590 | a(n) = A378762(A382499(n)). | [
"1",
"5",
"3",
"6",
"2",
"4",
"14",
"10",
"12",
"8",
"15",
"7",
"13",
"9",
"11",
"27",
"21",
"25",
"19",
"23",
"17",
"28",
"16",
"26",
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"22",
"44",
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"34",
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"33",
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"47",
"66",
"46",
"64",
"48",
"62",
"50",
"60",
"52",
"58",
"54",
"56"
]
| [
"nonn",
"tabf"
]
| 11 | 1 | 2 | [
"A000027",
"A000384",
"A016813",
"A056023",
"A376214",
"A378684",
"A378762",
"A379342",
"A379343",
"A380200",
"A380245",
"A380815",
"A380817",
"A381662",
"A381663",
"A381664",
"A381968",
"A382499",
"A382679",
"A382680",
"A383419",
"A383589",
"A383590",
"A383722",
"A383723",
"A383724"
]
| null | Boris Putievskiy, May 01 2025 | 2025-06-08T16:55:54 | oeisdata/seq/A383/A383590.seq | 5691c394a86b236e845c1fd4b4e212d1 |
A383591 | Smallest prime p where the absolute difference of the gaps to the adjacent primes exceeds n*log(p). | [
"7",
"113",
"1327",
"15683",
"31397",
"31397",
"360653",
"1349533",
"1357333",
"17051887",
"20831323",
"47326913",
"436273291",
"3842610773",
"3842610773",
"22367084959",
"25056082087",
"25056082087",
"304599509051",
"1346294310749"
]
| [
"nonn",
"hard",
"more"
]
| 25 | 1 | 1 | [
"A036263",
"A383215",
"A383216",
"A383591"
]
| null | Jean-Marc Rebert, May 03 2025 | 2025-05-10T09:18:51 | oeisdata/seq/A383/A383591.seq | 89b30e9533a6b46fc43cfd54132af47f |
A383592 | Positive integers k divisible by all positive integers whose decimal expansion appears as a substring of k. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"15",
"20",
"22",
"24",
"30",
"33",
"36",
"40",
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"48",
"50",
"55",
"60",
"66",
"70",
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"88",
"90",
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"100",
"110",
"120",
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"200",
"210",
"220",
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"300",
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"400",
"420",
"440",
"480",
"500",
"510",
"520",
"550",
"600",
"630",
"660",
"700",
"770",
"800",
"840",
"880"
]
| [
"nonn",
"base",
"easy"
]
| 16 | 1 | 2 | [
"A037124",
"A078546",
"A175381",
"A178157",
"A218978",
"A383592"
]
| null | Rémy Sigrist, May 01 2025 | 2025-05-13T11:33:49 | oeisdata/seq/A383/A383592.seq | ca73a9b64f0de517a0025898909175d1 |
A383593 | In the binary expansion of n, change the most significant 0 bit to 1, if there is any 0 bit. | [
"1",
"1",
"3",
"3",
"6",
"7",
"7",
"7",
"12",
"13",
"14",
"15",
"14",
"15",
"15",
"15",
"24",
"25",
"26",
"27",
"28",
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"28",
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"31",
"48",
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"50",
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"55",
"56",
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"59",
"60",
"61",
"62",
"63",
"56",
"57",
"58",
"59",
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"61",
"62",
"63",
"60",
"61",
"62",
"63",
"62",
"63",
"63",
"63",
"96",
"97",
"98",
"99",
"100"
]
| [
"nonn",
"base",
"easy",
"look"
]
| 34 | 0 | 3 | [
"A000225",
"A004760",
"A063250",
"A383593"
]
| null | Frederik P.J. Vandecasteele, Jun 11 2025 | 2025-06-18T00:53:49 | oeisdata/seq/A383/A383593.seq | 5dcd32f059fdbbdc92a5c6e969fb177e |
A383594 | a(0) = 0 and thereafter a(n) = 2 if a(n-1) is an odd prime, otherwise a(n) = a(n-1) + k where k = n - P(n) and P(n) is the number of odd primes among terms a(0),...,a(n-1). | [
"0",
"1",
"3",
"2",
"5",
"2",
"6",
"11",
"2",
"8",
"15",
"23",
"2",
"11",
"2",
"12",
"23",
"2",
"14",
"27",
"41",
"2",
"17",
"2",
"18",
"35",
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"2",
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"2",
"24",
"47",
"2",
"26",
"51",
"77",
"104",
"132",
"161",
"191",
"2",
"33",
"65",
"98",
"132",
"167",
"2",
"38",
"75",
"113",
"2",
"41",
"2",
"42",
"83",
"2",
"44",
"87",
"131",
"2",
"47",
"2",
"48",
"95",
"143",
"192",
"242"
]
| [
"nonn",
"new"
]
| 22 | 0 | 3 | null | null | Aaron Pieniozek, May 01 2025 | 2025-07-09T17:54:43 | oeisdata/seq/A383/A383594.seq | 40e8f55e0f76df05413e9004cfa2192e |
A383595 | a(n) is the smallest prime k such that (prime(n), k, u, v) are the vertices of a square in Ulam's spiral, where k < u < v are all primes; or -1 if there is no such k. | [
"-1",
"-1",
"-1",
"56527",
"59",
"67",
"251",
"-1",
"-1",
"2473",
"3001",
"43",
"43",
"41",
"173",
"1621",
"61",
"59",
"13",
"141937",
"13",
"13",
"10459",
"331",
"33211",
"643",
"179",
"41",
"41",
"1429",
"11",
"11",
"59",
"59",
"13",
"127",
"163",
"157",
"169957",
"47",
"103",
"56519",
"683",
"2843",
"6841",
"211",
"199",
"311",
"59407",
"439",
"11",
"137",
"274831"
]
| [
"sign"
]
| 13 | 1 | 4 | [
"A000040",
"A063826",
"A383595"
]
| null | Gonzalo Martínez, May 01 2025 | 2025-05-07T03:23:30 | oeisdata/seq/A383/A383595.seq | e2eca75eaa9c0cf7f9818fbe3a4cf368 |
A383596 | Integers in Ulam's spiral for which the numbers around them form a square whose four corners are all prime numbers. | [
"71",
"95",
"353",
"701",
"767",
"1151",
"1451",
"1961",
"2507",
"3347",
"4691",
"5957",
"7205",
"9671",
"13463",
"15635",
"21017",
"26051",
"27947",
"28985",
"34337",
"42017",
"49565",
"50921",
"52253",
"52349",
"55859",
"57191",
"63143",
"75857",
"79907",
"80831",
"81611",
"92339",
"101633",
"102557",
"106529",
"110495",
"114521",
"116513",
"121469",
"131075",
"136757",
"137879",
"14449"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A063826",
"A136626",
"A383595",
"A383596"
]
| null | Gonzalo Martínez, May 01 2025 | 2025-05-06T19:23:06 | oeisdata/seq/A383/A383596.seq | e5adfea7ab03dc908aef5e56993e64cd |
A383597 | Expansion of 1/( (1-x)^2 * (1-10*x) )^(1/3). | [
"1",
"4",
"25",
"190",
"1570",
"13552",
"120178",
"1085620",
"9940345",
"91962460",
"857750233",
"8053389142",
"76026759760",
"721017894640",
"6864725124520",
"65578937628304",
"628320730656586",
"6035594205744520",
"58110220504754650",
"560624083417180300",
"5418599393597801020",
"52459116546784350880"
]
| [
"nonn",
"easy"
]
| 21 | 0 | 2 | [
"A004987",
"A361375",
"A376802",
"A383597",
"A383598",
"A383599",
"A383601"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-04T15:07:13 | oeisdata/seq/A383/A383597.seq | 2ec0f0e9b13040a0faef578c68d0a528 |
A383598 | Expansion of 1/( (1-x^2)^2 * (1-x^2-9*x) )^(1/3). | [
"1",
"3",
"19",
"132",
"1000",
"7884",
"63802",
"525666",
"4388518",
"37010220",
"314633944",
"2692239012",
"23161121641",
"200158043223",
"1736461678195",
"15114944308560",
"131950690469920",
"1154858014686960",
"10130508263000440",
"89045875688728440",
"784127521246844872",
"6916291864328172336"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A376805",
"A383597",
"A383598",
"A383599"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-04T08:50:05 | oeisdata/seq/A383/A383598.seq | f888c05fb719ef4a6de6c7a4471b5dc5 |
A383599 | Expansion of 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3). | [
"1",
"3",
"18",
"127",
"951",
"7425",
"59473",
"484902",
"4005720",
"33425587",
"281152551",
"2380227705",
"20259341335",
"173218395228",
"1486747223136",
"12803424371263",
"110579924167533",
"957494150283249",
"8309596928695417",
"72260720257071936",
"629526082305028041",
"5493357757059584986"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A376806",
"A383597",
"A383598",
"A383599"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-04T14:44:30 | oeisdata/seq/A383/A383599.seq | 13ac13814de3d212bd7455202132b3c4 |
A383600 | Expansion of 1/( (1-x)^3 * (1-9*x) )^(1/4). | [
"1",
"3",
"15",
"97",
"699",
"5313",
"41689",
"334215",
"2721411",
"22423737",
"186497325",
"1562826195",
"13178010405",
"111700773135",
"951026829255",
"8128169277897",
"69701329848051",
"599462375836185",
"5169038197383789",
"44674793959777443",
"386916485124220929",
"3357265884164614707"
]
| [
"nonn",
"easy"
]
| 26 | 0 | 2 | [
"A004981",
"A084771",
"A231482",
"A383600",
"A383602"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-05T11:45:21 | oeisdata/seq/A383/A383600.seq | 2cc2c155db36664baf08265c1e39c5de |
A383601 | Expansion of 1/( (1-x) * (1-10*x)^2 )^(1/3). | [
"1",
"7",
"58",
"514",
"4705",
"43879",
"414208",
"3943492",
"37782346",
"363760390",
"3515819020",
"34088616940",
"331383573010",
"3228590970430",
"31514912933800",
"308126549765440",
"3016908101224105",
"29576113797737695",
"290271761086278610",
"2851684765215491050",
"28040613734007656545"
]
| [
"nonn",
"easy"
]
| 21 | 0 | 2 | [
"A004988",
"A377233",
"A383597",
"A383601",
"A383605",
"A383606"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-05T11:45:45 | oeisdata/seq/A383/A383601.seq | c45b5ec88e645e2fcc712c39d9618846 |
A383602 | Expansion of 1/( (1-x) * (1-9*x)^3 )^(1/4). | [
"1",
"7",
"55",
"453",
"3819",
"32637",
"281409",
"2441715",
"21285411",
"186225253",
"1633973125",
"14370441055",
"126631522005",
"1117707358515",
"9879287145855",
"87428272217853",
"774533435844531",
"6868083093333285",
"60952616213098789",
"541342619512077967",
"4811079933571973329"
]
| [
"nonn",
"easy"
]
| 22 | 0 | 2 | [
"A004982",
"A084771",
"A383600",
"A383602"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-05T16:21:48 | oeisdata/seq/A383/A383602.seq | f4cd86b738d5e0ad58f458393d573c9c |
A383603 | Expansion of 1/( (1-x)^2 * (1-x-9*x^2) )^(1/3). | [
"1",
"1",
"4",
"7",
"28",
"67",
"250",
"703",
"2497",
"7648",
"26488",
"85036",
"291337",
"960769",
"3280486",
"10993165",
"37541611",
"127077160",
"434707756",
"1481346064",
"5078811037",
"17388735001",
"59756049838",
"205310507773",
"707095964617",
"2436104710774",
"8406778618336",
"29027513057326"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A383597",
"A383603",
"A383604",
"A383605"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-06T00:52:13 | oeisdata/seq/A383/A383603.seq | 1f86e80a6c995252d7ed5886fb7c79a3 |
A383604 | Expansion of 1/( (1-x)^2 * (1-x-9*x^3) )^(1/3). | [
"1",
"1",
"1",
"4",
"7",
"10",
"31",
"70",
"127",
"328",
"799",
"1666",
"4000",
"9817",
"22078",
"52060",
"126727",
"296101",
"699601",
"1691350",
"4024450",
"9574393",
"23081776",
"55394488",
"132650923",
"319807159",
"770872429",
"1855190146",
"4479086230",
"10825202521",
"26145137668",
"63241928080",
"153144714331"
]
| [
"nonn"
]
| 18 | 0 | 4 | [
"A217615",
"A383597",
"A383603",
"A383604"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-06T09:32:51 | oeisdata/seq/A383/A383604.seq | 1af510a54a78ddff2a33d99a232e01b5 |
A383605 | Expansion of 1/( (1-x) * (1-x-9*x^2)^2 )^(1/3). | [
"1",
"1",
"7",
"13",
"64",
"160",
"661",
"1927",
"7288",
"23044",
"83413",
"275479",
"976198",
"3301462",
"11584861",
"39703783",
"138747637",
"479200129",
"1672353256",
"5803085008",
"20251472416",
"70486033288",
"246114881956",
"858397066324",
"2999541427177",
"10477699520329",
"36642516789607",
"128146441442989"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A383601",
"A383605",
"A383606"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-06T11:50:42 | oeisdata/seq/A383/A383605.seq | 2f158f850cce75613cb34d55b74f083a |
A383606 | Expansion of 1/( (1-x) * (1-x-9*x^3)^2 )^(1/3). | [
"1",
"1",
"1",
"7",
"13",
"19",
"70",
"166",
"307",
"853",
"2164",
"4600",
"11491",
"29137",
"66808",
"161692",
"403843",
"961129",
"2316238",
"5715742",
"13831219",
"33450073",
"82013692",
"199820584",
"485389276",
"1187152906",
"2900334583",
"7069398325",
"17283884710",
"42278723290",
"103291322056",
"252668924536"
]
| [
"nonn"
]
| 17 | 0 | 4 | [
"A383601",
"A383605",
"A383606"
]
| null | Seiichi Manyama, May 01 2025 | 2025-05-06T15:37:58 | oeisdata/seq/A383/A383606.seq | 750f6e1222be43fe6f1fc12b6276a25c |
A383607 | Square array read by antidiagonals upwards: T(n,k) is the smallest k-digit prime p such that nextprime(p) is a substring of p^n; or -1 if no such prime exists, n>1, k>0. | [
"-1",
"-1",
"23",
"-1",
"11",
"113",
"2",
"37",
"101",
"1123",
"7",
"17",
"487",
"2239",
"-1",
"5",
"47",
"-1",
"5659",
"34297",
"200003",
"3",
"13",
"-1",
"2399",
"91801",
"535487",
"-1",
"-1",
"31",
"607",
"1279",
"31627",
"842483",
"-1",
"-1",
"3",
"41",
"431",
"3163",
"12281",
"825059",
"6315629",
"59897017",
"714597769",
"-1",
"37",
"233",
"1931",
"15791",
"179947",
"5623421",
"-1",
"430784719",
"-1"
]
| [
"sign",
"tabl",
"base"
]
| 15 | 2 | 3 | [
"A052073",
"A052074",
"A052075",
"A052076",
"A274932",
"A383607"
]
| null | Jean-Marc Rebert, May 01 2025 | 2025-05-10T15:19:06 | oeisdata/seq/A383/A383607.seq | 51eeb8300b89fdd100b0669f3642f551 |
A383608 | Expansion of e.g.f. (1+x)*cosh(x)^2. | [
"1",
"1",
"2",
"6",
"8",
"40",
"32",
"224",
"128",
"1152",
"512",
"5632",
"2048",
"26624",
"8192",
"122880",
"32768",
"557056",
"131072",
"2490368",
"524288",
"11010048",
"2097152",
"48234496",
"8388608",
"209715200",
"33554432",
"905969664",
"134217728",
"3892314112",
"536870912",
"16642998272",
"2147483648",
"70866960384",
"8589934592"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 3 | [
"A081294",
"A229580",
"A383608"
]
| null | Enrique Navarrete, May 01 2025 | 2025-05-03T10:03:09 | oeisdata/seq/A383/A383608.seq | 5201892065b415226a2985c3cfcf2e27 |
A383609 | Triangle read by rows: T(n,k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k) for 0 < k < n, T(n,0) = T(n,n) = 1. | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"4",
"1",
"1",
"4",
"8",
"8",
"1",
"1",
"5",
"13",
"20",
"17",
"1",
"1",
"6",
"19",
"38",
"50",
"38",
"1",
"1",
"7",
"26",
"63",
"107",
"126",
"89",
"1",
"1",
"8",
"34",
"96",
"196",
"296",
"322",
"216",
"1",
"1",
"9",
"43",
"138",
"326",
"588",
"814",
"834",
"539",
"1",
"1",
"10",
"53",
"190",
"507",
"1052",
"1728",
"2236",
"2187",
"1374",
"1"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 5 | [
"A038185",
"A167630",
"A211278",
"A383609"
]
| null | Mélika Tebni, May 02 2025 | 2025-05-03T04:08:09 | oeisdata/seq/A383/A383609.seq | 20655e39e9a311fa04257049083159d3 |
A383610 | Expansion of 1/( (1-x^2) * (1-x^2-9*x)^2 )^(1/3). | [
"1",
"6",
"46",
"372",
"3106",
"26406",
"227179",
"1970952",
"17206552",
"150940848",
"1329193288",
"11741662152",
"103992267826",
"923052335316",
"8208568670644",
"73116321077784",
"652195543067596",
"5824848557238228",
"52080340709333998",
"466116121318516872",
"4175438344430632696"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A383598",
"A383601",
"A383610",
"A383611"
]
| null | Seiichi Manyama, May 02 2025 | 2025-05-03T03:07:43 | oeisdata/seq/A383/A383610.seq | ea3cfa6578e55c1a5cc07cee0c8d5ecf |
A383611 | Expansion of 1/( (1-x^3) * (1-x^3-9*x)^2 )^(1/3). | [
"1",
"6",
"45",
"361",
"2982",
"25083",
"213499",
"1832508",
"15827103",
"137356597",
"1196642427",
"10457750151",
"91630781245",
"804632867643",
"7078961780064",
"62380210284379",
"550478616300900",
"4863816606663882",
"43022548851457447",
"380930792260360182",
"3375853250109410583"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A383599",
"A383601",
"A383606",
"A383610",
"A383611"
]
| null | Seiichi Manyama, May 02 2025 | 2025-05-02T07:57:23 | oeisdata/seq/A383/A383611.seq | 3c8a5f26c751c9a5f3286e0dce7ae43d |
A383612 | Numbers k such that 2 + val(k!, 2) < p + val(k!, p), where p is the largest prime <= k and val(r, m) is the valuation of r at m. | [
"3",
"5",
"7",
"11",
"13",
"14",
"15",
"17",
"19",
"23",
"29",
"30",
"31",
"37",
"38",
"39",
"41",
"42",
"43",
"44",
"45",
"47",
"53",
"54",
"55",
"59",
"60",
"61",
"62",
"63",
"67",
"71",
"73",
"74",
"75",
"79",
"83",
"84",
"85",
"89",
"90",
"91",
"97",
"98",
"99",
"101",
"102",
"103",
"104",
"105",
"107",
"108",
"109",
"110",
"111",
"113",
"114",
"115",
"127",
"131",
"137",
"138",
"139",
"140",
"141",
"149",
"150"
]
| [
"nonn"
]
| 26 | 1 | 1 | [
"A000142",
"A007814",
"A007917",
"A383612"
]
| null | Ryan Jean, May 02 2025 | 2025-05-12T19:54:37 | oeisdata/seq/A383/A383612.seq | f8adc7a9271c7eadee3c52c03269b2bc |
A383613 | Square array read by antidiagonals upwards: T(n,k) (for n>1 and k>0) is the smallest k-digit prime p such that prevprime(p) appears as a substring in p^n; or -1 if no such prime exists. | [
"-1",
"3",
"-1",
"-1",
"17",
"-1",
"3",
"43",
"997",
"3701",
"3",
"31",
"607",
"2837",
"-1",
"3",
"11",
"929",
"5843",
"57349",
"-1",
"5",
"11",
"-1",
"4447",
"31063",
"224813",
"-1",
"5",
"-1",
"277",
"2477",
"77377",
"292223",
"9999991",
"65442077",
"7",
"11",
"809",
"7019",
"24379",
"262433",
"9862243",
"61879669",
"-1",
"-1",
"11",
"499",
"1571",
"17669",
"342281",
"1303613",
"32685743",
"763137931",
"-1"
]
| [
"sign",
"tabl",
"base"
]
| 13 | 2 | 2 | [
"A381969",
"A383613"
]
| null | Jean-Marc Rebert, May 02 2025 | 2025-05-09T23:12:48 | oeisdata/seq/A383/A383613.seq | e0734eabd7956ec91cbd9f656f6b2784 |
A383614 | The unique sequence such that Sum_{d|n} d*a(d)^(n/d) = sigma(n)^2 for every n. | [
"1",
"4",
"5",
"4",
"7",
"-10",
"9",
"-44",
"-23",
"-197",
"13",
"-845",
"15",
"-2340",
"-701",
"-9164",
"19",
"-31578",
"21",
"-124979",
"-11355",
"-381326",
"25",
"-1778580",
"-3323",
"-5162265",
"-212899",
"-21915630",
"31",
"-70256029",
"33",
"-311369996",
"-4439583",
"-1010580635",
"-129393",
"-4135827284",
"39",
"-14467258386"
]
| [
"sign",
"easy"
]
| 16 | 1 | 2 | [
"A000203",
"A072861",
"A383614"
]
| null | Yifan Xie, May 02 2025 | 2025-05-19T22:38:52 | oeisdata/seq/A383/A383614.seq | adedcf7a208ca2f1abd312d12aacc1fc |
A383615 | Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers. | [
"1",
"0",
"1",
"1",
"0",
"1",
"3",
"4",
"5",
"9",
"40",
"41",
"27",
"364",
"365",
"83",
"3444",
"3445",
"263",
"34584",
"34585",
"857",
"367224",
"367225",
"2859",
"4086940",
"4086941",
"9723",
"47268364",
"47268365",
"33591",
"564177640",
"564177641",
"117571",
"6911470020",
"6911470021",
"416023",
"86537568264",
"86537568265",
"1485799",
"1103799334200",
"1103799334201"
]
| [
"nonn",
"easy",
"tabf"
]
| 18 | 0 | 7 | [
"A000108",
"A131428",
"A381846",
"A383615",
"A383616"
]
| null | Miguel-Ángel Pérez García-Ortega, May 02 2025 | 2025-05-16T03:03:02 | oeisdata/seq/A383/A383615.seq | 0051e5c9ff5c513a934d59c058a9ab0a |
A383616 | Semiperimeter of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"1",
"1",
"6",
"45",
"378",
"3486",
"34716",
"367653",
"4088370",
"47273226",
"564194436",
"6911528806",
"86537776276",
"1103800077100",
"14305255952760",
"187980029453205",
"2500329620300130",
"33615543018643410",
"456277454997741300",
"6246438363690689010",
"86175353769957832380",
"1197196443763413093780",
"16738118900201817535560"
]
| [
"nonn",
"easy"
]
| 12 | 0 | 3 | [
"A000108",
"A131428",
"A381846",
"A383615",
"A383616"
]
| null | Miguel-Ángel Pérez García-Ortega, May 02 2025 | 2025-05-11T18:33:58 | oeisdata/seq/A383/A383616.seq | a7cfcbac13a62d4381eee63a01b09e6d |
A383617 | Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, k of which are picked out, 0 <= k <= n. | [
"1",
"2",
"2",
"10",
"16",
"10",
"104",
"272",
"272",
"104",
"3044",
"11456",
"16960",
"11456",
"3044",
"291968",
"1432608",
"2842304",
"2842304",
"1432608",
"291968",
"96928992",
"578431232",
"1441700480",
"1920352256",
"1441700480",
"578431232",
"96928992",
"112282908928",
"784780122880",
"2351993457920",
"3918054495616",
"3918054495616",
"2351993457920",
"784780122880",
"112282908928"
]
| [
"nonn",
"tabl"
]
| 14 | 0 | 2 | [
"A000595",
"A329874",
"A353996",
"A383617"
]
| null | Peter Dolland, May 02 2025 | 2025-05-08T03:15:05 | oeisdata/seq/A383/A383617.seq | 2748bbc91ec1bd4e13275007ef2b7eeb |
A383618 | Smallest prime gap whose first occurrence is >= 2^n. | [
"1",
"4",
"6",
"6",
"8",
"8",
"10",
"16",
"16",
"16",
"26",
"30",
"36",
"38",
"46",
"46",
"66",
"74",
"80",
"94",
"108",
"116",
"142",
"156",
"158",
"166",
"186",
"200",
"228",
"254",
"264",
"294",
"298",
"334",
"362",
"388",
"388",
"422",
"466",
"488",
"510",
"536",
"576",
"590",
"632",
"676",
"708",
"764",
"782",
"796",
"848",
"926",
"928",
"968",
"1006",
"1048"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A000230",
"A383618"
]
| null | Brian Kehrig, May 02 2025 | 2025-05-04T03:22:51 | oeisdata/seq/A383/A383618.seq | e04dcfed20f75dbad218aac76f0d1b19 |
A383619 | Conjectured list of least elements of nontrivial arithmetic derivative orbits. | [
"1",
"8",
"20",
"36",
"40",
"54",
"64",
"84",
"104",
"116",
"135",
"144",
"196",
"224",
"228",
"232",
"243",
"264",
"270",
"280"
]
| [
"nonn",
"more"
]
| 21 | 1 | 2 | [
"A003415",
"A068346",
"A099306",
"A258644",
"A258645",
"A258646",
"A258647",
"A258648",
"A258649",
"A258650",
"A383619"
]
| null | Dimitris Cardaris, May 02 2025 | 2025-05-14T17:49:32 | oeisdata/seq/A383/A383619.seq | 949310f8665d6ccf93b964b22e3d3661 |
A383620 | Number of weak compositions of n such that the set of adjacent differences is a subset of {-1,1}. | [
"1",
"4",
"5",
"9",
"13",
"20",
"30",
"45",
"66",
"102",
"152",
"229",
"344",
"518",
"780",
"1180",
"1775",
"2676",
"4037",
"6088",
"9182",
"13852",
"20891",
"31512",
"47536",
"71706",
"108166",
"163172",
"246140",
"371303",
"560118",
"844943",
"1274606",
"1922767",
"2900522",
"4375493",
"6600511",
"9956990",
"15020307",
"22658428"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A007318",
"A173258",
"A214247",
"A214249",
"A227310",
"A383620"
]
| null | John Tyler Rascoe, May 02 2025 | 2025-05-04T14:52:52 | oeisdata/seq/A383/A383620.seq | bade4e9fb523301dd5d2fa2cd410b7f3 |
A383621 | a(n) is the minimum possible value of x_1 + x_2 + ... + x_n where x_1, x_2, ..., x_n are positive integers such that x_i does not divide x_j for any i != j. | [
"1",
"5",
"10",
"17",
"28",
"41",
"55",
"72",
"91",
"111",
"134",
"159",
"187",
"216",
"247",
"282",
"319",
"360",
"403",
"447",
"493",
"540",
"589",
"641",
"694",
"749",
"808",
"869",
"934",
"1001",
"1069",
"1139",
"1210",
"1283",
"1359",
"1436",
"1515",
"1598",
"1683",
"1772",
"1863",
"1955",
"2050",
"2147",
"2245",
"2345",
"2446",
"2549",
"2656",
"2765",
"2878"
]
| [
"nonn",
"easy"
]
| 25 | 1 | 2 | [
"A027649",
"A383621",
"A383622"
]
| null | Yifan Xie, May 10 2025 | 2025-07-01T19:04:26 | oeisdata/seq/A383/A383621.seq | 9517b5c743d9dc13cefe2804bc20a6c5 |
A383622 | First differences of A383621. | [
"1",
"4",
"5",
"7",
"11",
"13",
"14",
"17",
"19",
"20",
"23",
"25",
"28",
"29",
"31",
"35",
"37",
"41",
"43",
"44",
"46",
"47",
"49",
"52",
"53",
"55",
"59",
"61",
"65",
"67",
"68",
"70",
"71",
"73",
"76",
"77",
"79",
"83",
"85",
"89",
"91",
"92",
"95",
"97",
"98",
"100",
"101",
"103",
"107",
"109",
"113",
"115",
"116",
"119",
"121",
"124",
"125",
"127",
"131",
"133",
"137",
"139",
"140",
"143"
]
| [
"nonn",
"easy"
]
| 22 | 1 | 2 | [
"A001047",
"A007310",
"A027649",
"A383621",
"A383622"
]
| null | Yifan Xie, May 10 2025 | 2025-05-20T10:21:57 | oeisdata/seq/A383/A383622.seq | aacdb0569e950ac2c45c8ab0d2a9a290 |
A383623 | a(n) = 4^n - (n^2 + 3*n + 4)*2^(n-2). | [
"0",
"0",
"2",
"20",
"128",
"672",
"3168",
"14016",
"59648",
"247808",
"1014272",
"4113408",
"16588800",
"66674688",
"267444224",
"1071497216",
"4289921024",
"17168596992",
"68694441984",
"274822594560",
"1099389992960",
"4397780172800",
"17591605133312",
"70367481692160",
"281472242024448"
]
| [
"nonn",
"easy"
]
| 10 | 0 | 3 | [
"A000302",
"A007466",
"A383623"
]
| null | Enrique Navarrete, May 03 2025 | 2025-05-08T22:26:28 | oeisdata/seq/A383/A383623.seq | a376e038e9b95c10a3fcb10de99fa709 |
A383624 | Expansion of 1/( Product_{k=0..3} (1 + (-1)^k * (2*k+1) * x) )^(1/4). | [
"1",
"1",
"11",
"31",
"275",
"1171",
"9061",
"47601",
"340851",
"2000035",
"13781041",
"85853021",
"581590621",
"3746717261",
"25226298475",
"165727074511",
"1114795372371",
"7412559559251",
"49931115844481",
"334625705273405",
"2259169929355945",
"15223239487082345",
"103033228974453295",
"697074803657176595"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A002426",
"A383624",
"A383625",
"A383626"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:35:00 | oeisdata/seq/A383/A383624.seq | 8ca4dfbd475e8ae33dd4ed1c82451253 |
A383625 | Expansion of 1/( Product_{k=0..7} (1 + (-1)^k * (2*k+1) * x) )^(1/8). | [
"1",
"1",
"43",
"127",
"4243",
"20371",
"560709",
"3642129",
"86291955",
"690569251",
"14567545105",
"135548975101",
"2614274677597",
"27191058449101",
"489590162677771",
"5534086571696943",
"94565644541691219",
"1137954908186418771",
"18691690961308817377",
"235813806878453147485",
"3760260498723044082985"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A002426",
"A383624",
"A383625",
"A383626"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-03T09:34:56 | oeisdata/seq/A383/A383625.seq | 0b8b3b46ea20fad830b65e0cc14ab8a1 |
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