This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375283 #9 Aug 10 2024 11:03:43
%S A375283 1,2,3,4,7,16,35,68,122,220,417,816,1588,3028,5707,10784,20547,39322,
%T A375283 75150,143144,272212,517990,987005,1881824,3586808,6832874,13013780,
%U A375283 24789200,47229672,89991518,171459667,326651952,622295173,1185547900,2258689217,4303264572
%N A375283 Expansion of 1/((1 - x - x^4)^2 - 4*x^5).
%H A375283 <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 A375283 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).
%F A375283 a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*n-6*k+2,2*k+1).
%o A375283 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^4)^2-4*x^5))
%o A375283 (PARI) a(n) = sum(k=0, n\4, binomial(2*n-6*k+2, 2*k+1))/2;
%Y A375283 Cf. A182890, A375278, A375285.
%Y A375283 Cf. A246883, A375282.
%K A375283 nonn
%O A375283 0,2
%A A375283 _Seiichi Manyama_, Aug 09 2024