A133416 a(n) = (1/10)*(2^(4*n-3)-5^n*F(2*n-1)+L(4*n-2)), where F() = Fibonacci numbers A000045 and L() = Lucas numbers A000032.

0, 0, 1, 91, 3060, 74613, 1562275, 30045016, 548354601, 9669627915, 166514967388, 2819214031645, 47139484522131, 780855182286336, 12842348655153745, 210042772449096763, 3420451064885308740, 55509625058510689221, 898396209147305575171, 14508414020570344661800

Offset

1,4

Links

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

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

Index entries for linear recurrences with constant coefficients, signature (38,-483,2286,-3065,400).

Formula

a(n) = Sum_{k = 0..floor((n-3)/5)} binomial(4n-2, 2n-10k-6).

G.f.: -x^3*(85*x^2+53*x+1) / ((16*x-1)*(x^2-7*x+1)*(25*x^2-15*x+1)). - Colin Barker, Apr 09 2013

Mathematica

LinearRecurrence[{38, -483, 2286, -3065, 400}, {0, 0, 1, 91, 3060}, 20] (* Harvey P. Dale, Jul 13 2022 *)

Prog

(PARI) a(n) = sum(k=0, (n-3)\5, binomial(4*n-2, 2*n-10*k-6)); \\ Michel Marcus, Sep 06 2017

Crossrefs

Sequence in context: A332949 A221738 A332913 * A169937 A047697 A096054

Adjacent sequences: A133413 A133414 A133415 * A133417 A133418 A133419

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 27 2007

Status

approved