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A036256
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a(n) = Sum_{i=0..n} binomial(i,floor(i/2)).
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9
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1, 2, 4, 7, 13, 23, 43, 78, 148, 274, 526, 988, 1912, 3628, 7060, 13495, 26365, 50675, 99295, 191673, 376429, 729145, 1434577, 2786655, 5490811, 10691111, 21091711, 41150011, 81266611, 158825371, 313942891, 614483086, 1215563476
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OFFSET
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0,2
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COMMENTS
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a(n-1) is the graph bandwidth of the n-hypercube graph Q_n. - Eric W. Weisstein, Jul 12 2011
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LINKS
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FORMULA
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a(n) ~ 2^(n+3/2) / sqrt(Pi*n) * (1 + (-1)^n/(12*n)). - Vaclav Kotesovec, Mar 02 2014
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MATHEMATICA
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Table[Sum[Binomial[k, Floor[k/2]], {k, 0, n}], {n, 0, 20}]
Table[Piecewise[{{(1/2)*(-1 - I*Sqrt[3] - (3*Gamma[3 + n]*Hypergeometric2F1Regularized[1, (3 + n)/2, (4 + n)/2, 4])/Gamma[2 + n/2]), Mod[n, 2] == 0}, {((-1 - I*Sqrt[3])*Gamma[(1 + n)/2] - 4*n!*(Hypergeometric2F1Regularized[1, (2 + n)/2, (3 + n)/2, 4] + (2 + n)*Hypergeometric2F1Regularized[1, (4 + n)/2, (5 + n)/2, 4]))/(2*Gamma[(1 + n)/2]), Mod[n, 2] == 1}}], {n, 0, 20}] // Expand
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PROG
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(PARI) for(n=0, 50, print1(sum(k=0, n, binomial(k, floor(k/2))), ", ")) \\ G. C. Greubel, Jan 24 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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