A078040 Expansion of (1-x)/(1+x-2*x^2+2*x^3).

1, -2, 4, -10, 22, -50, 114, -258, 586, -1330, 3018, -6850, 15546, -35282, 80074, -181730, 412442, -936050, 2124394, -4821378, 10942266, -24833810, 56361098, -127913250, 290303066, -658851762, 1495284394, -3393594050, 7701866362, -17479623250, 39670544074, -90033523298

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

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

Crossrefs

First differences of A077970.

Programs

Mathematica

CoefficientList[Series[(1-x)/(1+x-2x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-1,2,-2},{1,-2,4},40] (* Harvey P. Dale, Dec 09 2011 *)

PARI

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

Formula

a(0) = 1, a(1) = -2, a(2) = 4, a(n) = -a(n-1) + 2*a(n-2) - 2*a(n-3) for n > 2. - Harvey P. Dale, Dec 09 2011

a(n) = A077970(n)-A077970(n-1). - R. J. Mathar, Mar 19 2025