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 A352045 #9 May 30 2022 09:55:18
%S A352045 1,1,1,1,2,5,11,22,43,85,170,341,683,1367,2744,5552,11381,23729,50423,
%T A352045 109220,240845,539411,1223357,2800535,6451340,14915084,34533851,
%U A352045 79949741,184865936,426627122,982217705,2255539406,5166125852,11802977573,26903285366
%N A352045 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(k).
%H A352045 Seiichi Manyama, <a href="/A352045/b352045.txt">Table of n, a(n) for n = 0..1000</a>
%F A352045 G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x).
%F A352045 E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(3*n) / (3*n)! dx.
%t A352045 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 3 k] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 34}]
%t A352045 nmax = 34; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A352045 Cf. A351970, A352044.
%K A352045 nonn
%O A352045 0,5
%A A352045 _Ilya Gutkovskiy_, Mar 01 2022