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 A375308 #17 Aug 11 2024 22:04:10
%S A375308 1,1,7,30,137,644,2936,13625,62701,289547,1335378,6161329,28424456,
%T A375308 131135696,604991601,2791106585,12876698159,59406240678,274068969337,
%U A375308 1264408966284,5833313285128,26911817257385,124156868897413,572794023175795,2642568194952474
%N A375308 a(n) = Sum_{k=0..floor(2*n/3)} binomial(4*n-4*k,2*k).
%H A375308 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,11,6,-6,4,-1).
%F A375308 a(n) = A375279(2*n).
%F A375308 a(n) = A375314(2*n).
%F A375308 a(n) = 2*a(n-1) + 11*a(n-2) + 6*a(n-3) - 6*a(n-4) + 4*a(n-5) - a(n-6).
%F A375308 G.f.: (1 - x - 6*x^2 - x^3)/((1 - x + 2*x^2 - x^3)^2 - 16*x^2).
%o A375308 (PARI) a(n) = sum(k=0, 2*n\3, binomial(4*n-4*k, 2*k));
%o A375308 (PARI) my(N=30, x='x+O('x^N)); Vec((1-x-6*x^2-x^3)/((1-x+2*x^2-x^3)^2-16*x^2))
%Y A375308 Cf. A108479, A375279, A375307, A375314.
%K A375308 nonn
%O A375308 0,3
%A A375308 _Seiichi Manyama_, Aug 11 2024