A360090 a(n) = Sum_{k=0..n} binomial(5*k,n-k).

1, 1, 6, 21, 71, 251, 882, 3088, 10829, 37975, 133146, 466852, 1636944, 5739647, 20125051, 70564951, 247423522, 867546829, 3041899638, 10665883415, 37398034921, 131129599227, 459782762029, 1612146986543, 5652708454881, 19820223058176, 69496108849357

Offset

0,3

Comments

The number of ways to place non-overlapping Young diagrams of shape (2,1,1,1,1) on an 9 by n rectangle. - Per Alexandersson, Jul 01 2025

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1,5,10,10,5,1).

Formula

a(n) = a(n-1) + 5*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).

G.f.: 1/(1 - x*(1+x)^5).

Maple

seq(add(binomial(5*k, n-k), k=0..n), n=0..50); # Robert Israel, Jul 09 2025

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*k, n-k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x*(1+x)^5))

Crossrefs

Cf. A002478, A099234, A099235.

Sequence in context: A022814 A000390 A000391 * A107660 A200665 A200466

Adjacent sequences: A360087 A360088 A360089 * A360091 A360092 A360093

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 25 2023

Status

approved