A135990 Expansion of x^3*(x-1)*(x+1) / (x^5-2*x^4+x^2-1).

0, 0, 1, 0, 0, 0, -2, 1, -2, 1, 2, -3, 7, -7, 4, 1, -13, 22, -28, 24, -1, -33, 77, -109, 103, -44, -84, 251, -399, 442, -275, -144, 774, -1427, 1766, -1414, 74, 2214, -4885, 6808, -6447, 2454, 5537, -16047, 25239, -27402, 16619, 10229, -49906, 90272, -110546, 86433, -505, -144017, 310859, -427429, 398302

Offset

1,7

Links

Table of n, a(n) for n=1..57.

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

Formula

G.f.: x^3*(x-1)*(x+1) / (x^5-2*x^4+x^2-1). [Colin Barker, Feb 02 2013]

Mathematica

v[0] = {0, 0, 1}; v[1] = {0, 1, 2};
M0 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}};
N0 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}};
v[n_] := v[n] = N0.v[n - 1] - M0.v[n - 2]
Table[v[n][[1]], {n, 0, 100}]

Crossrefs

Sequence in context: A080916 A071622 A182063 * A347256 A392217 A347224

Adjacent sequences: A135987 A135988 A135989 * A135991 A135992 A135993

Keyword

sign,easy,less

Author

Roger L. Bagula, Mar 03 2008

Extensions

Better name from Colin Barker, Feb 02 2013

Status

approved