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 A375279 #11 Aug 10 2024 11:04:08
%S A375279 1,1,1,2,7,16,30,61,137,303,644,1365,2936,6340,13625,29209,62701,
%T A375279 134758,289547,621816,1335378,2868341,6161329,13233947,28424456,
%U A375279 61052489,131135696,281667368,604991601,1299458257,2791106585,5995020362,12876698159,27657838272
%N A375279 Expansion of (1 - x - x^3)/((1 - x - x^3)^2 - 4*x^4).
%H A375279 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,2,0,-1).
%F A375279 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).
%F A375279 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k,2*k).
%o A375279 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x-x^3)/((1-x-x^3)^2-4*x^4))
%o A375279 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-4*k, 2*k));
%Y A375279 Cf. A108479, A375278.
%K A375279 nonn
%O A375279 0,4
%A A375279 _Seiichi Manyama_, Aug 09 2024