A077963 Expansion of 1/(1+x^2+2*x^3).

1, 0, -1, -2, 1, 4, 3, -6, -11, 0, 23, 22, -23, -68, -21, 114, 157, -72, -385, -242, 529, 1012, -45, -2070, -1979, 2160, 6119, 1798, -10439, -14036, 6843, 34914, 21229, -48600, -91057, 6142, 188257, 175972, -200541, -552486, -151403, 953568, 1256375, -650762, -3163511, -1861988, 4465035

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 (0,-1,-2).

Crossrefs

Cf. A077912.

Programs

GAP

a:=[1,0,-1];; for n in [4..50] do a[n]:=-a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 23 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x^2+2*x^3) )); // G. C. Greubel, Jun 23 2019

Mathematica

CoefficientList[Series[1/(1+x^2+2*x^3), {x,0,50}], x] (* or *) LinearRecurrence[{0,-1,-2}, {1,0,-1}, 50] (* G. C. Greubel, Jun 23 2019 *)

PARI

my(x='x+O('x^50)); Vec(1/(1+x^2+2*x^3)) \\ G. C. Greubel, Jun 23 2019

Sage

(1/(1+x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 23 2019

Formula

a(n) = (-1)^n * A077912(n). - G. C. Greubel, Jun 23 2019