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 A351144 #6 Feb 03 2022 10:43:01
%S A351144 1,0,1,3,10,39,181,972,5797,37389,258202,1905681,15016465,125920872,
%T A351144 1117950913,10452866439,102485649754,1050464300187,11231883627301,
%U A351144 125055844922916,1447371528438565,17382103226123313,216221862096537994,2781342531957176085,36942930754308211969
%N A351144 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
%C A351144 Shifts 2 places left under 3rd-order binomial transform.
%F A351144 a(0) = 1, a(1) = 0; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 3^k * a(n-k-2).
%t A351144 nmax = 24; A[_] = 0; Do[A[x_] = 1 + x^2 A[x/(1 - 3 x)]/(1 - 3 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351144 a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[Binomial[n - 2, k] 3^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 24}]
%Y A351144 Cf. A000994, A004212, A351049, A351143, A351150, A351151, A351152.
%K A351144 nonn
%O A351144 0,4
%A A351144 _Ilya Gutkovskiy_, Feb 02 2022