A077987 Expansion of 1/(1+2*x-x^2+2*x^3).

1, -2, 5, -14, 37, -98, 261, -694, 1845, -4906, 13045, -34686, 92229, -245234, 652069, -1733830, 4610197, -12258362, 32594581, -86667918, 230447141, -612751362, 1629285701, -4332217046, 11519222517, -30629233482, 81442123573, -216551925662, 575804441861, -1531045056530

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 (-2,1,-2).

Crossrefs

Cf. A077938.

Programs

GAP

a:=[1,-2,5];; for n in [4..40] do a[n]:=-2*a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+2*x-x^2+2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

CoefficientList[Series[1/(1+2x-x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-2,1,-2},{1,-2,5},40] (* Harvey P. Dale, Dec 27 2013 *)

PARI

Vec(1/(1+2*x-x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

(1/(1+2*x-x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(n) = -2*a(n-1)+a(n-2)-2*a(n-3) with a(0)=1, a(1)=-2, a(2)=5. - Harvey P. Dale, Dec 27 2013

a(n) = (-1)^n * A077938(n). - G. C. Greubel, Jun 25 2019