A133415 a(n) = (1/10)*(2^(4*n-1)-5^n*L(2*n)+L(4*n)), where L() = Lucas numbers A000032.

0, 0, 12, 560, 15504, 346104, 6906900, 129024512, 2310796740, 40226003064, 686392118544, 11543525003120, 192052217662812, 3169185696976320, 51968632068982524, 848016349271816384, 13784507849163060240, 223382961205435729512, 3611184426083530971300, 58264040214444951056384

Offset

1,3

Links

Table of n, a(n) for n=1..20.

H.-J. Seiffert, Problem H-651, Fib. Quart., 45 (2007), 91.

Formula

a(n) = Sum_{k = 0..floor((n-3)/5)} binomial(4n, 2n-10k-5).

O.g.f.: -4*x^3*(3+26*x+5*x^2)/((-1+16*x)*(1-15*x+25*x^2)*(1-7*x+x^2)) = -(1/20)+(1/10)*(-2+15*x)/(1-15*x+25*x^2)-(1/20)/(-1+16*x)+(1/10)*(2-7*x)/(1-7*x+x^2) . - R. J. Mathar, Nov 28 2007

Prog

(PARI) a(n) = sum(k=0, (n-3)\5, binomial(4*n, 2*n-10*k-5)); \\ Michel Marcus, Sep 06 2017

Crossrefs

Sequence in context: A193381 A224539 A210816 * A192602 A227143 A274259

Adjacent sequences: A133412 A133413 A133414 * A133416 A133417 A133418

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2007

Status

approved