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 A352042 #6 Mar 02 2022 08:46:01
%S A352042 1,1,1,1,2,3,4,6,9,13,19,28,41,61,93,144,226,359,574,920,1475,2361,
%T A352042 3769,6000,9528,15100,23897,37789,59739,94446,149365,236322,374073,
%U A352042 592357,938311,1486625,2355620,3732704,5914682,9371599,14847866,23522460,37262742,59026662
%N A352042 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-2*k-1,k) * a(k).
%F A352042 G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)) / (1 - x).
%t A352042 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 2 k - 1, k] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 43}]
%t A352042 nmax = 43; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A352042 Cf. A119262, A352043.
%K A352042 nonn
%O A352042 0,5
%A A352042 _Ilya Gutkovskiy_, Mar 01 2022