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 A351342 #6 Feb 16 2022 04:16:13
%S A351342 1,1,1,1,3,9,27,83,271,971,3865,16879,78985,388385,1987201,10561385,
%T A351342 58443891,337724057,2040085491,12862712499,84357800063,573182197539,
%U A351342 4021203303593,29062345301487,216129411635057,1653180368063361,13003920016983361,105158133803473329
%N A351342 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 * A(x/(1 - 2*x)) / (1 - 2*x).
%C A351342 Shifts 3 places left under 2nd-order binomial transform.
%F A351342 a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * 2^k * a(n-k-3).
%t A351342 nmax = 27; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x/(1 - 2 x)]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351342 a[n_] := a[n] = If[n < 3, 1, Sum[Binomial[n - 3, k] 2^k a[n - k - 3], {k, 0, n - 3}]]; Table[a[n], {n, 0, 27}]
%Y A351342 Cf. A000996, A000998, A004211, A007472, A210540, A351343, A351344, A351345.
%K A351342 nonn
%O A351342 0,5
%A A351342 _Ilya Gutkovskiy_, Feb 08 2022