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 A375314 #9 Aug 11 2024 22:04:06
%S A375314 1,0,1,4,7,12,30,68,137,292,644,1380,2936,6324,13625,29216,62701,
%T A375314 134784,289547,621708,1335378,2868620,6161329,13233352,28424456,
%U A375314 61053608,131135696,281665480,604991601,1299461088,2791106585,5995016764,12876698159,27657841516
%N A375314 a(n) = Sum_{k=0..floor(n/2)} binomial(4*k,n-2*k).
%H A375314 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,4,6,4,1).
%F A375314 a(n) = a(n-2) + 4*a(n-3) + 6*a(n-4) + 4*a(n-5) + a(n-6).
%F A375314 G.f.: 1/(1 - x^2*(1 + x)^4).
%o A375314 (PARI) a(n) = sum(k=0, n\2, binomial(4*k, n-2*k));
%o A375314 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^2*(1+x)^4))
%Y A375314 Cf. A116090.
%K A375314 nonn,easy
%O A375314 0,4
%A A375314 _Seiichi Manyama_, Aug 11 2024