OFFSET
0,2
COMMENTS
Equals row sums of triangle A145972. - Gary W. Adamson, Oct 25 2008
a(n-1) is the graph bandwidth of the n-hypercube graph Q_n. - Eric W. Weisstein, Jul 12 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
L. H. Harper, Optimal numberings and isoperimetric problems on graphs, J. Comb. Th. 1 (1966), 385-393.
Eric Weisstein's World of Mathematics, Graph Bandwidth
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
G.f.: 2/((1-z)*(1-2*z+sqrt(1-4*z^2))). - Emeric Deutsch, Nov 25 2003
a(n) ~ 2^(n+3/2) / sqrt(Pi*n) * (1 + (-1)^n/(12*n)). - Vaclav Kotesovec, Mar 02 2014
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
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n, binomial(k, floor(k/2))), ", ")) \\ G. C. Greubel, Jan 24 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved