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 A375285 #11 Aug 10 2024 11:03:37
%S A375285 1,2,3,4,5,8,17,36,69,120,196,320,547,980,1786,3216,5661,9804,16932,
%T A375285 29472,51820,91602,161767,284424,498103,871150,1525380,2676544,
%U A375285 4703158,8265354,14514236,25464576,44656997,78324398,137430720,241225072,423451668,743244866
%N A375285 Expansion of 1/((1 - x - x^5)^2 - 4*x^6).
%H A375285 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,2,2,0,0,0,-1).
%F A375285 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-5) + 2*a(n-6) - a(n-10).
%F A375285 a(n) = (1/2) * Sum_{k=0..floor(n/5)} binomial(2*n-8*k+2,2*k+1).
%o A375285 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^5)^2-4*x^6))
%o A375285 (PARI) a(n) = sum(k=0, n\5, binomial(2*n-8*k+2, 2*k+1))/2;
%Y A375285 Cf. A182890, A375278, A375283.
%Y A375285 Cf. A246884.
%K A375285 nonn
%O A375285 0,2
%A A375285 _Seiichi Manyama_, Aug 09 2024