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 A352879 #14 Apr 09 2022 09:49:28
%S A352879 1,1,2,3,5,10,21,44,94,207,463,1034,2289,5023,10952,23784,51550,
%T A352879 111707,242370,527176,1150643,2522064,5553977,12290257,27326784,
%U A352879 61031999,136860175,307979631,695115874,1572737222,3565447689,8095730133,18405209484
%N A352879 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(k).
%F A352879 G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x)^2.
%F A352879 E.g.f.: 1 + exp(x) * Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)!.
%t A352879 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 32}]
%t A352879 nmax = 32; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
%Y A352879 Cf. A040027, A119685, A352045, A352904.
%K A352879 nonn
%O A352879 0,3
%A A352879 _Ilya Gutkovskiy_, Apr 07 2022