A135259 a(n) = 3*A131666(n) - A131666(n+1).

0, -1, 2, 1, 3, 2, 7, 13, 30, 57, 115, 226, 455, 909, 1822, 3641, 7283, 14562, 29127, 58253, 116510, 233017, 466035, 932066, 1864135, 3728269, 7456542, 14913081, 29826163, 59652322, 119304647, 238609293, 477218590, 954437177, 1908874355, 3817748706

Offset: 0

Author

Paul Curtz, Dec 01 2007

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

Crossrefs

Cf. A131666.

Programs

GAP

a:=[0,-1,2,1];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-3]+2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019

Magma

R:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019

Maple

seq(coeff(series(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)), x, n+1), x, n), n = 0 .. 35); # G. C. Greubel, Nov 21 2019

Mathematica

LinearRecurrence[{2,0,-1,2}, {0,-1,2,1}, 35] (* G. C. Greubel, Oct 05 2016 *)

PARI

concat(0, Vec(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) + O(x^35))) \\ Michel Marcus, Oct 05 2016

Sage

def A135259_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2))).list()
A135259_list(35) # G. C. Greubel, Nov 21 2019

Formula

A131666(n) - a(n) = A092220(n).

O.g.f.: x*(1-x)*(1 -3*x)/( (2*x-1)*(x+1)*(1 -x +x^2) ). - R. J. Mathar, Jul 22 2008

a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - G. C. Greubel, Oct 05 2016

Extensions

Edited and extended by R. J. Mathar, Jul 22 2008