A375283 - OEIS

%I #9 Aug 10 2024 11:03:43

%S 1,2,3,4,7,16,35,68,122,220,417,816,1588,3028,5707,10784,20547,39322,

%T 75150,143144,272212,517990,987005,1881824,3586808,6832874,13013780,

%U 24789200,47229672,89991518,171459667,326651952,622295173,1185547900,2258689217,4303264572

%N Expansion of 1/((1 - x - x^4)^2 - 4*x^5).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,2,2,0,0,-1).

%F a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).

%F a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*n-6*k+2,2*k+1).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^4)^2-4*x^5))

%o (PARI) a(n) = sum(k=0, n\4, binomial(2*n-6*k+2, 2*k+1))/2;

%Y Cf. A182890, A375278, A375285.

%Y Cf. A246883, A375282.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 09 2024