A078013 Expansion of (1-x)/(1-x+x^3).

1, 0, 0, -1, -1, -1, 0, 1, 2, 2, 1, -1, -3, -4, -3, 0, 4, 7, 7, 3, -4, -11, -14, -10, 1, 15, 25, 24, 9, -16, -40, -49, -33, 7, 56, 89, 82, 26, -63, -145, -171, -108, 37, 208, 316, 279, 71, -245, -524, -595, -350, 174, 769, 1119, 945, 176, -943, -1888, -2064, -1121, 767, 2831, 3952, 3185, 354, -3598, -6783, -7137

Offset

0,9

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = -A050935(n).

a(n+1) = a(n) - a(n-2), a(0)=1, a(1)=a(2)=0. - Philippe Deléham, Nov 12 2011

G.f.: 1 - x^3 - x^4 + x^6 + x^6/(G(0) - 1) where G(k) = 1 - x*(k+1)/(1 - x/(x - (k+1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 17 2012

Mathematica

LinearRecurrence[{1, 0, -1}, {1, 0, 0}, 70] (* or *) CoefficientList[Series[ (1-x)/(1-x+x^3), {x, 0, 70}], x] (* G. C. Greubel, Jun 29 2019 *)

Prog

(PARI) Vec((1-x)/(1-x+x^3)+O(x^70)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1-x)/(1-x+x^3) )); // G. C. Greubel, Jun 29 2019
(Sage) ((1-x)/(1-x+x^3)).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019
(GAP) a:=[1, 0, 0];; for n in [4..70] do a[n]:=a[n-1]-a[n-3]; od; a; # G. C. Greubel, Jun 29 2019

Crossrefs

Cf. A050935.

Sequence in context: A247917 A050935 A104769 * A086461 A047089 A122218

Adjacent sequences: A078010 A078011 A078012 * A078014 A078015 A078016

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved