A077872 Expansion of 1 / ((1-x)*(1-x+x^2+x^3)).

1, 2, 2, 0, -3, -4, 0, 8, 13, 6, -14, -32, -23, 24, 80, 80, -23, -182, -238, -32, 389, 660, 304, -744, -1707, -1266, 1186, 4160, 4241, -1104, -9504, -12640, -2031, 20114, 34786, 16704, -38195, -89684, -68192, 59688, 217565, 226070, -51182, -494816, -669703, -123704, 1040816, 1834224, 917113

Offset

0,2

Links

Table of n, a(n) for n=0..48.

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

Formula

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-4) for n>3. - Colin Barker, Jun 20 2017

Mathematica

CoefficientList[Series[1/((1-x)(1-x+x^2+x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -2, 0, 1}, {1, 2, 2, 0}, 50] (* Harvey P. Dale, May 23 2021 *)

Prog

(PARI) Vec(1 / ((1-x)*(1-x+x^2+x^3)) + O(x^50)) \\ Colin Barker, Jun 20 2017

Crossrefs

Sequence in context: A191362 A137422 A139139 * A300453 A239292 A262879

Adjacent sequences: A077869 A077870 A077871 * A077873 A077874 A077875

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved