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%I #7 Jun 29 2023 18:43:47
%S 1,4,20,120,800,5600,40000,288000,2080000,15040000,108800000,
%T 787200000,5696000000,41216000000,298240000000,2158080000000,
%U 15616000000000,112998400000000,817664000000000,5916672000000000,42813440000000000
%N Third binomial transform of Fibonacci(3n-1) (A015448).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -20).
%F G.f.: (1-6x)/(1-10x+20x^2).
%F a(n) = (5-sqrt(5))*(5+sqrt(5))^n/10 + (5+sqrt(5))*(5-sqrt(5))^n/10.
%F a(n) = 2^n*A093129(n).
%Y Cf. A000045, A015448, A093129.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 23 2004