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.

A368891 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(n-2*k,k).

Original entry on oeis.org

1, 1, 1, 4, 9, 16, 61, 183, 433, 1603, 5581, 15951, 59449, 225928, 738893, 2827321, 11387617, 41174086, 163185805, 686315474, 2680560361, 11035625413, 48086847117, 199640217719, 853587430801, 3836667616201, 16739402030989, 74206353913480
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2 - n/2, -n/2}, -27*n/4], {n, 0, 30}] (* Vaclav Kotesovec, Jan 09 2024 *)
  • PARI
    a(n) = sum(k=0, n\3, n^k*binomial(n-2*k, k));

Formula

a(n) = [x^n] 1/(1 - x - n*x^3).
a(n) ~ exp(n^(2/3)/3 + n^(1/3)/18) * n^(n/3) / 3 * (1 + 2/(3*n^(1/3)) + 2/(9*n^(2/3))). - Vaclav Kotesovec, Jan 09 2024