%I #11 Feb 04 2026 04:55:03

%S 1,4,20,120,800,5600,40000,288000,2080000,15040000,108800000,

%T 787200000,5696000000,41216000000,298240000000,2158080000000,

%U 15616000000000,112998400000000,817664000000000,5916672000000000,42813440000000000,309800960000000000,2241740800000000000

%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.: (1-6*x)/(1-10*x+20*x^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).

%F E.g.f.: exp(5*x) * (cosh(sqrt(5)*x) - sinh(sqrt(5)*x)/sqrt(5)). - _Amiram Eldar_, Feb 03 2026

%t LinearRecurrence[{10, -20}, {1, 4}, 25] (* _Amiram Eldar_, Feb 03 2026 *)

%Y Cf. A000045, A015448, A093129.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 23 2004