A077920 Expansion of (1-x)^(-1)/(1+2*x-x^2-x^3).

1, -1, 4, -7, 18, -38, 88, -195, 441, -988, 2223, -4992, 11220, -25208, 56645, -127277, 285992, -642615, 1443946, -3244514, 7290360, -16381287, 36808421, -82707768, 185842671, -417584688, 938304280, -2108350576, 4737420745, -10644887785, 23918845740, -53745158519, 120764274994

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

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

Programs

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1+2x-x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-1,3,0,-1},{1,-1,4,-7},40] (* Harvey P. Dale, Mar 13 2013 *)

PARI

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

Formula

a(n) = (-1)^n*A124400(n). - Philippe Deléham, Dec 18 2006

a(n) = a(n-1) + 3*a(n-2) - a(n-4); a(0)=1, a(1)=-1, a(2)=4, a(3)=-7. - Harvey P. Dale, Mar 13 2013