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 A120462 Expansion of -2*x*(-3-2*x+4*x^2) / ((x-1)*(2*x+1)*(2*x-1)*(1+x)). 1
 0, 6, 4, 22, 20, 86, 84, 342, 340, 1366, 1364, 5462, 5460, 21846, 21844, 87382, 87380, 349526, 349524, 1398102, 1398100, 5592406, 5592404, 22369622, 22369620, 89478486, 89478484, 357913942, 357913940, 1431655766, 1431655764, 5726623062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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]. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4). FORMULA a(2*n+1) = A047849(n+2). a(2*n)= 2*A020988(n). - R. J. Mathar, Nov 07 2011 From Colin Barker, Sep 09 2016: (Start) a(n) = -2*(1/6 + (-2)^n/3 + (-1)^n/2 - 2^n). a(n) = 5*a(n-2)-4*a(n-4) for n>3. (End) MATHEMATICA 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}] PROG (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 CROSSREFS Sequence in context: A185734 A292696 A318209 * A236602 A169689 A328757 Adjacent sequences:  A120459 A120460 A120461 * A120463 A120464 A120465 KEYWORD nonn,easy AUTHOR Roger L. Bagula and Gary W. Adamson, Jun 28 2006 STATUS approved

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Last modified June 24 00:14 EDT 2021. Contains 345403 sequences. (Running on oeis4.)