A055519 - OEIS

A055519

a(n) = 9*a(n-1) + 33*a(n-2) - 76*a(n-3) - 33*a(n-4) + 9*a(n-5) + a(n-6), a(0)=a(1)=1, a(2)=2, a(3)=35, a(4)=312, a(5)=3779.

1, 1, 2, 35, 312, 3779, 41590, 474169, 5342808, 60450145, 682988978, 7720432691, 87256315920, 986227664411, 11146765278382, 125986353493225, 1423957841588232, 16094263592763889, 181905138292910570, 2055979904686591259, 23237679087969620328, 262643489044489470155

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (9,33,-76,-33,9,1).

FORMULA

a(n) = Sum_{k=1..n} Fibonacci(k)^5*a(n-k), a(0)=1. - Vladeta Jovovic, Apr 23 2003

G.f.: (x^2+x-1)*(x^2+11*x-1)*(x^2-4*x-1)/(x^6+9*x^5-33*x^4-76*x^3+33*x^2+9*x-1). - Alois P. Heinz, Oct 24 2021

MATHEMATICA

LinearRecurrence[{9, 33, -76, -33, 9, 1}, {1, 1, 2, 35, 312, 3779}, 20] (* Harvey P. Dale, Oct 20 2021 *)

CROSSREFS