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A105872
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a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k, n).
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8
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Sum[Binomial[2n-3k, n], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Harvey P. Dale, Jan 13 2015 *)
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PROG
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(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k, n)); \\ Seiichi Manyama, Jan 28 2023
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Erroneous title changed by Paul Barry, Apr 14 2010
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STATUS
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approved
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