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A105872 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k, n). 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A294816 A263790 A247416 * A304781 A148490 A006612
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

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Last modified June 21 23:34 EDT 2024. Contains 373560 sequences. (Running on oeis4.)