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 A120463 #19 Dec 29 2023 10:59:37
%S A120463 0,1,1,4,6,13,21,40,66,121,201,364,606,1093,1821,3280,5466,9841,16401,
%T A120463 29524,49206,88573,147621,265720,442866,797161,1328601,2391484,
%U A120463 3985806,7174453,11957421,21523360,35872266,64570081,107616801,193710244
%N A120463 Expansion of x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).
%C A120463 Top element of the vector obtained by multiplying the n-th power of the 5 X 5 matrix [[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3].
%H A120463 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-3).
%F A120463 G.f.: x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).
%F A120463 a(2n+2) = A134931(n). a(2n+1) = A003462(n+1). - _R. J. Mathar_, Nov 07 2011
%t A120463 LinearRecurrence[{0,4,0,-3},{0,1,1,4,6},40] (* _Harvey P. Dale_, Dec 15 2018 *)
%Y A120463 Cf. A003462, A134931.
%K A120463 nonn,easy
%O A120463 0,4
%A A120463 _Roger L. Bagula_ and _Gary W. Adamson_, Jun 30 2006