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 A352039 #6 Mar 02 2022 08:44:07
%S A352039 1,1,1,2,3,4,6,9,13,20,32,51,82,133,215,346,555,886,1408,2231,3528,
%T A352039 5572,8797,13892,21950,34707,54919,86958,137761,218339,346178,549073,
%U A352039 871261,1383243,2197542,3494019,5560580,8858687,14128865,22560717,36067022,57725840
%N A352039 a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * a(k).
%F A352039 G.f. A(x) satisfies: A(x) = A(x^3/(1 - x)) / (1 - x).
%t A352039 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 2 k, k] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 41}]
%t A352039 nmax = 41; A[_] = 1; Do[A[x_] = A[x^3/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A352039 Cf. A092684, A102547, A352041.
%K A352039 nonn
%O A352039 0,4
%A A352039 _Ilya Gutkovskiy_, Mar 01 2022