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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 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

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