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 A375278 #12 Aug 10 2024 11:04:13
%S A375278 1,2,3,6,15,34,70,146,317,690,1480,3162,6788,14608,31395,67392,144701,
%T A375278 310854,667793,1434310,3080542,6616676,14212315,30526804,65567936,
%U A375278 140832740,302495240,649730544,1395554885,2997508382,6438345511,13828920758,29703127299
%N A375278 Expansion of 1/((1 - x - x^3)^2 - 4*x^4).
%H A375278 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,2,0,-1).
%F A375278 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).
%F A375278 a(n) = (1/2) * Sum_{k=0..floor(n/3)} binomial(2*n-4*k+2,2*k+1).
%o A375278 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^3)^2-4*x^4))
%o A375278 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-4*k+2, 2*k+1))/2;
%Y A375278 Cf. A182890, A375283, A375285.
%Y A375278 Cf. A246840, A375279.
%K A375278 nonn
%O A375278 0,2
%A A375278 _Seiichi Manyama_, Aug 09 2024