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

0,4

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).

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

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 *)

Prog

(PARI) Vec((1-x)/(1+x^2-x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1+x^2-x^3) )); // G. C. Greubel, Aug 05 2019
(Sage) ((1-x)/(1+x^2-x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019
(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

Crossrefs

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

Sequence in context: A051613 A173291 A341889 * A077961 A077962 A353484

Adjacent sequences: A078028 A078029 A078030 * A078032 A078033 A078034

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved