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 A120462 #16 Jul 28 2024 12:14:35
%S A120462 0,6,4,22,20,86,84,342,340,1366,1364,5462,5460,21846,21844,87382,
%T A120462 87380,349526,349524,1398102,1398100,5592406,5592404,22369622,
%U A120462 22369620,89478486,89478484,357913942,357913940,1431655766,1431655764,5726623062
%N A120462 Expansion of -2*x*(-3-2*x+4*x^2) / ((x-1)*(2*x+1)*(2*x-1)*(1+x)).
%C A120462 Top element of the vector obtained by multiplying the n-th power of the 6 X 6 matrix [[0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3, 5].
%H A120462 Colin Barker, <a href="/A120462/b120462.txt">Table of n, a(n) for n = 0..1000</a>
%H A120462 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).
%F A120462 a(2*n+1) = A047849(n+2). a(2*n)= 2*A020988(n). - _R. J. Mathar_, Nov 07 2011
%F A120462 From _Colin Barker_, Sep 09 2016: (Start)
%F A120462 a(n) = -2*(1/6 + (-2)^n/3 + (-1)^n/2 - 2^n).
%F A120462 a(n) = 5*a(n-2)-4*a(n-4) for n>3.
%F A120462 (End)
%t A120462 M = {{0, 1, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {1, 0, 0, 0, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
%t A120462 LinearRecurrence[{0,5,0,-4},{0,6,4,22},40] (* _Harvey P. Dale_, Jul 28 2024 *)
%o A120462 (PARI) concat(0, Vec(2*x*(3+2*x-4*x^2)/((1-x)*(1+x)*(1-2*x)*(1+2*x)) + O(x^40))) \\ _Colin Barker_, Sep 09 2016
%K A120462 nonn,easy
%O A120462 0,2
%A A120462 _Roger L. Bagula_ and _Gary W. Adamson_, Jun 28 2006