A139469 a(n) = Sum_{k=0..n} C(n,3k+2)^2.

0, 0, 1, 9, 36, 101, 261, 882, 3921, 17253, 67554, 243695, 876789, 3324906, 13166791, 52301709, 203824548, 782913717, 3010327497, 11695756698, 45823049817, 179787741723, 703527078258, 2747647985241, 10739885115573, 42082084255050, 165225573240651

Offset: 0

Author

N. J. A. Sloane, Jun 12 2008

Keywords

• nonn

Comments

The recurrence is same as for A119363. - Vaclav Kotesovec, Mar 12 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A024495, A119363, A139468.

Programs

Magma

[&+[Binomial(n, 3*k+2)^2: k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Mar 14 2019

Mathematica

Table[Sum[Binomial[n, 3*k + 2]^2, {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Mar 12 2019 *)

PARI

a(n) = sum(k=0, n, binomial(n, 3*k+2)^2); \\ Michel Marcus, Mar 12 2019

Formula

a(n) ~ 4^n / (3*sqrt(Pi*n)). - Vaclav Kotesovec, Mar 12 2019