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A135259 a(n) = 3*A131666(n) - A131666(n+1). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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

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 *)

PROG

(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

(MAGMA) R<x>:=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

(Sage)

def A135259_list(prec):

    P.<x> = 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

(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

CROSSREFS

Cf. A131666.

Sequence in context: A101709 A005247 A280104 * A122147 A141486 A184344

Adjacent sequences:  A135256 A135257 A135258 * A135260 A135261 A135262

KEYWORD

sign

AUTHOR

Paul Curtz, Dec 01 2007

EXTENSIONS

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

STATUS

approved

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Last modified July 5 20:10 EDT 2020. Contains 335473 sequences. (Running on oeis4.)