A077971 Expansion of 1/(1+x-x^2-2*x^3).

1, -1, 2, -1, 1, 2, -3, 7, -6, 7, 1, -6, 21, -25, 34, -17, 1, 50, -83, 135, -118, 87, 65, -214, 453, -537, 562, -193, -319, 1250, -1955, 2567, -2022, 679, 2433, -5798, 9589, -10521, 8514, 143, -12671, 29842, -42227, 46727, -29270, -8457, 72641, -139638, 195365, -189721, 105810, 95199, -368831

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,1,2).

Crossrefs

Cf. A077948.

First differences of A077901.

Programs

GAP

a:=[1,-1,2];; for n in [4..60] do a[n]:=-a[n-1]+a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jun 24 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/(1+x-x^2-2*x^3) )); // G. C. Greubel, Jun 24 2019

Mathematica

LinearRecurrence[{-1,1,2}, {1,-1,2}, 60] (* or *) CoefficientList[Series[ 1/(1 +x-x^2-2*x^3), {x,0,60}], x] (* G. C. Greubel, Jun 24 2019 *)

PARI

Vec(1/(1+x-x^2-2*x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1+x-x^2-2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019

Formula

a(n) = (-1)^n * A077948(n). - G. C. Greubel, Jun 24 2019