A087423 a(n) = S(3*n,3)/S(n,3) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).

32, 768, 20672, 565248, 15491072, 424685568, 11643256832, 319215894528, 8751751626752, 239941585993728, 6578336360824832, 180354352643309568, 4944668491903926272, 135565048129674805248, 3716706651755063017472, 101898745479045492768768

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (32,-128,64).

Formula

a(n) = 4^n + (14+6*sqrt(5))^n + (14-6*sqrt(5))^n.

G.f.: -32*x*(6*x^2-8*x+1) / ((4*x-1)*(16*x^2-28*x+1)). - Colin Barker, Dec 01 2012

Mathematica

LinearRecurrence[{32, -128, 64}, {32, 768, 20672}, 20] (* Harvey P. Dale, Feb 17 2018 *)

Crossrefs

Cf. A020876.

Sequence in context: A283695 A283127 A295713 * A004384 A248071 A183215

Adjacent sequences: A087420 A087421 A087422 * A087424 A087425 A087426

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 22 2003

Status

approved