A077883 Expansion of (1-x)^(-1)/(1-x^2+x^3).

1, 1, 2, 1, 2, 0, 2, -1, 3, -2, 5, -4, 8, -8, 13, -15, 22, -27, 38, -48, 66, -85, 115, -150, 201, -264, 352, -464, 617, -815, 1082, -1431, 1898, -2512, 3330, -4409, 5843, -7738, 10253, -13580, 17992, -23832, 31573, -41823, 55406, -73395, 97230, -128800, 170626, -226029, 299427, -396654

Offset

0,3

Links

Table of n, a(n) for n=0..51.

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

Formula

G.f.: (1-x)^(-1)/(1-x^2+x^3).

a(n) = a(n-1) + a(n-2) - 2*a(n-3) + a(n-4) with a(0)=1, a(1)=1, a(2)=2, a(3)=1. - Harvey P. Dale, Mar 26 2012

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-x^2+x^3), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -2, 1}, {1, 1, 2, 1}, 60] (* Harvey P. Dale, Mar 26 2012 *)

Prog

(PARI) Vec((1-x)^(-1)/(1-x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A029357 A118054 A322019 * A058666 A112181 A151676

Adjacent sequences: A077880 A077881 A077882 * A077884 A077885 A077886

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved