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A036256
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Sum(i=0..n, binomial(i,floor(i/2)) ).
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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equals row sums of triangle A145972 [From Gary W. Adamson, Oct 25 2008]
a(n-1) is the graph bandwidth of the n-hypercube graph Q_n [From Eric Weisstein, Jul 12 2011]
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REFERENCES
| L. H. Harper, Optimal numberings and isoperimetric problems on graphs, J. Comb. Th. 1 (1966), 385-393.
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FORMULA
| G.f.: 2/((1-z)*(1-2*z+sqrt(1-4*z^2))). - Emeric Deutsch, Nov 25 2003
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MATHEMATICA
| 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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CROSSREFS
| Partial sums of A001405.
A145972 [From Gary W. Adamson, Oct 25 2008]
Sequence in context: A048888 A026724 A054163 * A093629 A174566 A018182
Adjacent sequences: A036253 A036254 A036255 * A036257 A036258 A036259
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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