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%I A093132 #17 Sep 08 2022 08:45:13
%S A093132 1,8,60,440,3200,23200,168000,1216000,8800000,63680000,460800000,
%T A093132 3334400000,24128000000,174592000000,1263360000000,9141760000000,
%U A093132 66150400000000,478668800000000,3463680000000000,25063424000000000
%N A093132 Third binomial transform of Fibonacci(3n+2).
%H A093132 G. C. Greubel, Table of n, a(n) for n = 0..1000
%H A093132 Index entries for linear recurrences with constant coefficients, signature (10,-20).
%F A093132 G.f.: (1-2*x)/(1-10*x+20*x^2).
%F A093132 a(n) = ( (5 + 3*sqrt(5))*(5 + sqrt(5))^n + (5 - 3*sqrt(5))*(5 - sqrt(5))^n)/10.
%F A093132 a(n) = 2^n*A039717(n).
%F A093132 a(2*n) = 4^n*5^n*Fibonacci(2*n+2), a(2*n+1) = 2^(2*n+1)*5^n*Lucas(2*n+3). - _G. C. Greubel_, Dec 27 2019
%p A093132 seq(coeff(series((1-2*x)/(1-10*x+20*x^2), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Dec 27 2019
%t A093132 Table[If[EvenQ[n], 2^n*5^(n/2)*Fibonacci[n+2], 2^n*5^((n-1)/2)*LucasL[n+2]], {n, 0, 30}] (* _G. C. Greubel_, Dec 27 2019 *)
%o A093132 (PARI) my(x='x+O('x^30)); Vec((1-2*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Dec 27 2019
%o A093132 (Magma) I:=[1,8]; [n le 2 select I[n] else 10*(Self(n-1) - 2*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Dec 27 2019
%o A093132 (Sage)
%o A093132 def A093132_list(prec):
%o A093132 P.