A105872 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k, n).

1, 2, 6, 21, 75, 273, 1009, 3770, 14202, 53846, 205216, 785460, 3017106, 11624580, 44905518, 173863965, 674506059, 2621371005, 10203609597, 39773263035, 155231706951, 606554343495, 2372544034143, 9289131196485, 36401388236461

Offset

0,2

Links

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

Formula

G.f.: 2/(4*x^2+sqrt(1-4*x)*(3*x+1)-5*x+1). - Vladimir Kruchinin, May 24 2014

Conjecture: -3*(n+1)*(7*n-2)*a(n) +6*(7*n+5)*(2*n-1)*a(n-1) -(n+1)*(7*n-2)*a(n-2) +2*(7*n+5)*(2*n-1)*a(n-3)=0. - R. J. Mathar, Nov 28 2014

a(n) ~ 2^(2*n+3) / (7*sqrt(Pi*n)). - Vaclav Kotesovec, Jan 28 2023

a(n) = [x^n] 1/((1-x^3) * (1-x)^(n+1)). - Seiichi Manyama, Apr 08 2024

Mathematica

Table[Sum[Binomial[2n-3k, n], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Harvey P. Dale, Jan 13 2015 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k, n)); \\ Seiichi Manyama, Jan 28 2023

Crossrefs

Cf. A144904, A360150, A360151, A360152, A360153.

Sequence in context: A294816 A263790 A247416 * A304781 A148490 A006612

Adjacent sequences: A105869 A105870 A105871 * A105873 A105874 A105875

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2005

Extensions

Erroneous title changed by Paul Barry, Apr 14 2010

Name corrected by Seiichi Manyama, Jan 28 2023

Status

approved