cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A373718 Expansion of 1/(1 - x * (1 + x^2)^3).

Original entry on oeis.org

1, 1, 1, 4, 7, 13, 28, 53, 105, 211, 413, 819, 1624, 3206, 6349, 12565, 24851, 49183, 97315, 192539, 380989, 753836, 1491567, 2951330, 5839638, 11554621, 22862658, 45237262, 89508951, 177107406, 350434385, 693388850, 1371977475, 2714670141, 5371396171
Offset: 0

Views

Author

Seiichi Manyama, Jun 15 2024

Keywords

Crossrefs

Column k=3 of A373717.
Cf. A373720.

Programs

  • PARI
    a(n) = sum(k=0, 3*n\7, binomial(3*n-6*k, k));

Formula

a(n) = a(n-1) + 3*a(n-3) + 3*a(n-5) + a(n-7).
a(n) = Sum_{k=0..floor(3*n/7)} binomial(3*n-6*k,k).

A373719 a(n) = Sum_{k=0..floor(n^2/(2*n+1))} binomial(n * (n-2*k),k).

Original entry on oeis.org

1, 1, 1, 4, 9, 26, 91, 281, 1105, 4105, 16576, 70643, 301405, 1382928, 6363876, 30605836, 150820769, 758835104, 3941917840, 20787546715, 112615930451, 620969188400, 3492709446326, 20034747631656, 116780977502105, 693539635192626, 4181549476945504, 25627647913369903
Offset: 0

Views

Author

Seiichi Manyama, Jun 15 2024

Keywords

Crossrefs

Main diagonal of A373717.
Cf. A099237.

Programs

  • PARI
    a(n) = sum(k=0, n^2\(2*n+1), binomial(n*(n-2*k), k));

Formula

a(n) = [x^n] 1/(1 - x * (1 + x^2)^n).
Showing 1-2 of 2 results.