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

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

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).

Crossrefs

Cf. A077950.

Programs

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

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^3) )); // G. C. Greubel, Jun 29 2019

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 *)

PARI

my(x='x+O('x^50)); Vec((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

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