A077962 Expansion of 1/(1+x^2+x^3).

1, 0, -1, -1, 1, 2, 0, -3, -2, 3, 5, -1, -8, -4, 9, 12, -5, -21, -7, 26, 28, -19, -54, -9, 73, 63, -64, -136, 1, 200, 135, -201, -335, 66, 536, 269, -602, -805, 333, 1407, 472, -1740, -1879, 1268, 3619, 611, -4887, -4230, 4276, 9117, -46, -13393, -9071, 13439, 22464, -4368, -35903, -18096, 40271, 53999

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
• M. Janjic, Determinants and Recurrence Sequences, Journal of Integer Sequences, 2012, Article 12.3.5. [_N. J. A. Sloane_, Sep 16 2012]
• Index entries for linear recurrences with constant coefficients, signature (0,-1,-1).

Programs

GAP

a:=[1,0,-1];; for n in [4..70] do a[n]:=-a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jun 23 2019

Magma

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(1+x^2+x^3) )); // G. C. Greubel, Jun 23 2019

Mathematica

CoefficientList[ Series[1/(1 + x^2 + x^3), {x, 0, 70}], x] (* Robert G. Wilson v, Mar 22 2011 *)
LinearRecurrence[{0,-1,-1},{1,0,-1},70] (* Harvey P. Dale, Dec 04 2015 *)

PARI

Vec(1/(1+x^2+x^3)+O(x^70)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1+x^2+x^3)).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jun 23 2019

Formula

a(n) = (-1)^n*A077961(n).