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 A373640 #9 Jun 12 2024 08:22:06
%S A373640 1,1,1,2,5,8,12,24,45,76,134,246,440,775,1386,2490,4437,7902,14128,
%T A373640 25248,45042,80396,143604,256410,457704,817209,1459215,2605267,
%U A373640 4651330,8304787,14827872,26473839,47266965,84392484,150677220,269022969,480322072,857583545
%N A373640 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-8*k,k).
%H A373640 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,0,0,-3,0,0,1).
%F A373640 G.f.: 1 / (1 - x^3 - x/(1 - x^3)^2).
%F A373640 a(n) = a(n-1) + 3*a(n-3) - 3*a(n-6) + a(n-9) for n > 8.
%o A373640 (PARI) a(n) = sum(k=0, n\3, binomial(3*n-8*k, k));
%Y A373640 Cf. A000930, A373639.
%K A373640 nonn,easy
%O A373640 0,4
%A A373640 _Seiichi Manyama_, Jun 12 2024