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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.
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%I #23 Oct 24 2021 12:28:51

%S 1,1,2,35,312,3779,41590,474169,5342808,60450145,682988978,7720432691,

%T 87256315920,986227664411,11146765278382,125986353493225,

%U 1423957841588232,16094263592763889,181905138292910570,2055979904686591259,23237679087969620328,262643489044489470155

%N 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.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,33,-76,-33,9,1).

%F a(n) = Sum_{k=1..n} Fibonacci(k)^5*a(n-k), a(0)=1. - _Vladeta Jovovic_, Apr 23 2003

%F 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

%t LinearRecurrence[{9,33,-76,-33,9,1},{1,1,2,35,312,3779},20] (* _Harvey P. Dale_, Oct 20 2021 *)

%Y Cf. A000045, A054894, A055518, A056572, A215928.

%K easy,nonn

%O 0,3

%A _Barry Cipra_, Jul 04 2000

%E a(0)=1 prepended and edited by _Alois P. Heinz_, Oct 24 2021