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 A376718 #9 Oct 03 2024 09:56:55
%S A376718 1,1,1,1,4,11,22,37,61,114,232,467,894,1660,3096,5893,11351,21803,
%T A376718 41535,78778,149615,285100,544165,1037963,1977196,3764056,7167911,
%U A376718 13657244,26027280,49594720,94481929,179981485,342872893,653244245,1244600984,2371227307
%N A376718 Expansion of (1 - x + x^4)/((1 - x + x^4)^2 - 4*x^4).
%H A376718 <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 A376718 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).
%F A376718 a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k+1,2*k).
%o A376718 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^4)/((1-x+x^4)^2-4*x^4))
%o A376718 (PARI) a(n) = sum(k=0, n\4, binomial(2*n-6*k+1, 2*k));
%Y A376718 Cf. A000302, A376716, A376717.
%Y A376718 Cf. A375283.
%K A376718 nonn
%O A376718 0,5
%A A376718 _Seiichi Manyama_, Oct 02 2024