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%I #18 Mar 26 2024 14:45:17
%S 32,768,20672,565248,15491072,424685568,11643256832,319215894528,
%T 8751751626752,239941585993728,6578336360824832,180354352643309568,
%U 4944668491903926272,135565048129674805248,3716706651755063017472,101898745479045492768768
%N a(n) = S(3*n,3)/S(n,3) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (32,-128,64).
%F a(n) = 4^n + (14+6*sqrt(5))^n + (14-6*sqrt(5))^n.
%F G.f.: -32*x*(6*x^2-8*x+1) / ((4*x-1)*(16*x^2-28*x+1)). - _Colin Barker_, Dec 01 2012
%t LinearRecurrence[{32,-128,64},{32,768,20672},20] (* _Harvey P. Dale_, Feb 17 2018 *)
%Y Cf. A020876.
%K nonn,easy
%O 1,1
%A _Benoit Cloitre_, Oct 22 2003
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