A077959 Expansion of 1/(1+2*x^3).

1, 0, 0, -2, 0, 0, 4, 0, 0, -8, 0, 0, 16, 0, 0, -32, 0, 0, 64, 0, 0, -128, 0, 0, 256, 0, 0, -512, 0, 0, 1024, 0, 0, -2048, 0, 0, 4096, 0, 0, -8192, 0, 0, 16384, 0, 0, -32768, 0, 0, 65536, 0, 0, -131072, 0, 0, 262144, 0, 0, -524288, 0, 0, 1048576, 0, 0, -2097152, 0, 0, 4194304, 0, 0, -8388608, 0

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..1002
• Index entries for linear recurrences with constant coefficients, signature (0, 0, -2).

Crossrefs

Cf. A077958.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/(1+2*x^3) )); // G. C. Greubel, Jun 23 2019

Mathematica

CoefficientList[Series[1/(1+2x^3),{x,0,80}],x] (* or *) LinearRecurrence[ {0,0,-2},{1,0,0},80] (* Harvey P. Dale, Dec 19 2012 *)

PARI

Vec(1/(1+2*x^3)+O(x^80)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

(1/(1+2*x^3)).series(x, 80).coefficients(x, sparse=False) # G. C. Greubel, Jun 23 2019

Formula

a(0)=1, a(1)=0, a(2)=0, a(n) = -2*a(n-3). - Harvey P. Dale, Dec 19 2012

a(n) = (-1)^n * A077958(n). - R. J. Mathar, Mar 04 2018