A078031 Expansion of (1-x)/(1 + x^2 - x^3).

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

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

The Ca2 sums, see A180662, of triangle A108299 equal the terms of this sequence. - Johannes W. Meijer, Aug 14 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,-1,1).

Crossrefs

Cf. A077961, A108299, A180662. - Johannes W. Meijer, Aug 14 2011

Programs

GAP

a:=[1,-1,-1];; for n in [4..60] do a[n]:=-a[n-2]+a[n-3]; od; a; # G. C. Greubel, Aug 05 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1+x^2-x^3) )); // G. C. Greubel, Aug 05 2019

Maple

A078031 := proc(n) option remember: coeftayl((1-x)/(1+x^2-x^3),x=0,n) end: seq(A078031(n), n=0..60); # Johannes W. Meijer, Aug 14 2011

Mathematica

CoefficientList[Series[(1-x)/(1+x^2-x^3),{x,0,60}],x] (* or *) LinearRecurrence[{0,-1,1},{1,-1,-1},60] (* Harvey P. Dale, Apr 08 2012 *)

PARI

Vec((1-x)/(1+x^2-x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

((1-x)/(1+x^2-x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019

Formula

G.f.: (1-x)/(1 + x^2 - x^3).

a(n) = -a(n-2) + a(n-3); a(0)=1, a(1)=-1, a(2)=-1. - Harvey P. Dale, Apr 08 2012