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 A351344 #6 Feb 16 2022 04:15:51
%S A351344 1,1,1,1,1,1,3,9,27,81,243,731,2223,6939,22727,79971,306929,1282815,
%T A351344 5744361,26984415,130656409,644739377,3224303841,16318576681,
%U A351344 83717193681,436948772697,2331807007139,12791837178265,72472130039123,425239734375217,2584950704996379
%N A351344 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - 2*x)) / (1 - 2*x).
%C A351344 Shifts 5 places left under 2nd-order binomial transform.
%F A351344 a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-5,k) * 2^k * a(n-k-5).
%t A351344 nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x/(1 - 2 x)]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351344 a[n_] := a[n] = If[n < 5, 1, Sum[Binomial[n - 5, k] 2^k a[n - k - 5], {k, 0, n - 5}]]; Table[a[n], {n, 0, 30}]
%Y A351344 Cf. A004211, A007472, A010749, A210542, A275935, A351342, A351343, A351345.
%K A351344 nonn
%O A351344 0,7
%A A351344 _Ilya Gutkovskiy_, Feb 08 2022