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 A375307 #12 Aug 11 2024 22:05:01
%S A375307 1,1,4,16,52,194,685,2452,8771,31327,112004,400285,1430710,5113647,
%T A375307 18277014,65325542,233485250,834519021,2982723523,10660798289,
%U A375307 38103641048,136189372297,486765693153,1739789499591,6218325456983,22225431015537,79437750107600
%N A375307 a(n) = Sum_{k=0..floor(3*n/5)} binomial(3*n-3*k,2*k).
%H A375307 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,5,3,-3,1).
%F A375307 a(n) = A116090(2*n).
%F A375307 a(n) = 2*a(n-1) + 5*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5).
%F A375307 G.f.: (1 - x - 3*x^2)/(1 - 2*x - 5*x^2 - 3*x^3 + 3*x^4 - x^5).
%o A375307 (PARI) a(n) = sum(k=0, 3*n\5, binomial(3*n-3*k, 2*k));
%o A375307 (PARI) my(N=30, x='x+O('x^N)); Vec((1-x-3*x^2)/(1-2*x-5*x^2-3*x^3+3*x^4-x^5))
%Y A375307 Cf. A108479, A116090, A375308.
%K A375307 nonn
%O A375307 0,3
%A A375307 _Seiichi Manyama_, Aug 11 2024