A077974 Expansion of 1/(1+x+2*x^3).

1, -1, 1, -3, 5, -7, 13, -23, 37, -63, 109, -183, 309, -527, 893, -1511, 2565, -4351, 7373, -12503, 21205, -35951, 60957, -103367, 175269, -297183, 503917, -854455, 1448821, -2456655, 4165565, -7063207, 11976517, -20307647, 34434061, -58387095, 99002389, -167870511, 284644701

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,0,-2).

Crossrefs

Signed version of A077949.

Programs

GAP

a:=[1,-1,1];; for n in [4..45] do a[n]:=-a[n-1]-2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 45); Coefficients(R!( 1/(1+x+2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

CoefficientList[Series[1/(1+x+2*x^3),{x,0,45}],x] (* or *) LinearRecurrence[ {-1,0,-2},{1,-1,1},45] (* Harvey P. Dale, Aug 29 2012 *)

PARI

Vec(1/(1+x+2*x^3)+O(x^45)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1+x+2*x^3)).series(x, 45).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(0)=1, a(1)=-1, a(2)=1, a(n)=a(n-1)-2*a(n-3). - Harvey P. Dale, Aug 29 2012