A078014 Expansion of (1-x)/(1-x+2*x^3).

1, 0, 0, -2, -2, -2, 2, 6, 10, 6, -6, -26, -38, -26, 26, 102, 154, 102, -102, -410, -614, -410, 410, 1638, 2458, 1638, -1638, -6554, -9830, -6554, 6554, 26214, 39322, 26214, -26214, -104858, -157286, -104858, 104858, 419430, 629146, 419430, -419430, -1677722, -2516582, -1677722, 1677722

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,-2).

Formula

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

G.f.: G(0)/(2*(1+x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 25 2013

a(n) = A077950(n) - A077950(n-1). - R. J. Mathar, Jul 21 2016

Mathematica

LinearRecurrence[{1, 0, -2}, {1, 0, 0}, 50] (* or *) CoefficientList[Series[ (1-x)/(1-x+2*x^3), {x, 0, 50}], x] (* G. C. Greubel, Jun 29 2019 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x+2*x^3)) \\ G. C. Greubel, Jun 29 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^3) )); // G. C. Greubel, Jun 29 2019
(Sage) ((1-x)/(1-x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019
(GAP) a:=[1, 0, 0];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-3]; od; a; # G. C. Greubel, Jun 29 2019

Crossrefs

Cf. A077950.

Sequence in context: A230096 A116564 A323442 * A063867 A024723 A035470

Adjacent sequences: A078011 A078012 A078013 * A078015 A078016 A078017

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved