login
Expansion of (1 - x - x^4)/((1 - x - x^4)^2 - 4*x^5).
3

%I #7 Aug 10 2024 11:04:03

%S 1,1,1,1,2,7,16,29,47,82,162,331,650,1220,2262,4261,8175,15747,30121,

%T 57210,108521,206456,393865,751675,1432772,2728076,5193901,9893596,

%U 18853664,35928972,68454369,130403085,248413549,473261209,901681650,1717923403,3272944760

%N Expansion of (1 - x - x^4)/((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) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k,2*k).

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

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

%Y Cf. A375279.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Aug 09 2024