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

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A375364, A375372.

Programs

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 *)

PARI

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

PARI

a(n) = (-1)^n*sum(k=0, n\2, binomial(k-1, n-2*k)); \\ Seiichi Manyama, Aug 14 2024

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

a(n) = (-1)^n * Sum_{k=0..floor(n/2)} binomial(k-1,n-2*k). - Seiichi Manyama, Aug 14 2024