A122822 The (1,4) entry in the matrix M^n, where M is the 4 X 4 matrix [[0,-1,1,0],[0,0,-1,1],[1,1,1,0],[0,1,1,1]].

0, 0, -1, 0, 0, -1, 1, 2, 3, 10, 19, 35, 71, 131, 240, 446, 810, 1467, 2660, 4792, 8621, 15501, 27814, 49873, 89384, 160079, 286589, 512943, 917813, 1641978, 2937132, 5253248, 9395035, 16801268, 30044388, 53724067, 96064297, 171769178, 307129259, 549150614, 981877515, 1755576755, 3138916347

Offset

0,8

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,1,-3).

Formula

a(n) = 2*a(n-1) + a(n-3) - 3*a(n-4) for n>=4; a(0)=0, a(1)=-1, a(2)=0, a(3)=0.

G.f.: -x^2*(1 - 2*x) / (1 - 2*x - x^3 + 3*x^4). - Colin Barker, Mar 03 2017

Maple

a[0]:=0: a[1]:=0: a[2]:=-1: a[3]:=0: for n from 4 to 42 do a[n]:=2*a[n-1]+a[n-3]-3*a[n-4] od: seq(a[n], n=0..42);

Mathematica

M = {{0, -1, 1, 0}, {0, 0, -1, 1}, {1, 1, 1, 0}, {0, 1, 1, 1}}; v[1] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]

Prog

(PARI) concat(vector(2), Vec(-x^2*(1 - 2*x) / (1 - 2*x - x^3 + 3*x^4) + O(x^50))) \\ Colin Barker, Mar 03 2017

Crossrefs

Sequence in context: A329850 A175569 A275020 * A295951 A083944 A306106

Adjacent sequences: A122819 A122820 A122821 * A122823 A122824 A122825

Keyword

sign,easy

Author

Gary W. Adamson and Roger L. Bagula, Oct 20 2006

Extensions

Edited by N. J. A. Sloane, Oct 26 2006

Status

approved