A122099 a(n) = -3*a(n-1) + a(n-3) for n>2, with a(0)=1, a(1)=1, a(2)=0.

1, 1, 0, 1, -2, 6, -17, 49, -141, 406, -1169, 3366, -9692, 27907, -80355, 231373, -666212, 1918281, -5523470, 15904198, -45794313, 131859469, -379674209, 1093228314, -3147825473, 9063802210, -26098178316, 75146709475, -216376326215, 623030800329, -1793945691512, 5165460748321

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (-3,0,1).

Formula

G.f.: (1+4*x+3*x^2)/(1+3*x-x^3).

a(n) = (-1)^n*A122100(n). - R. J. Mathar, Sep 27 2014

Maple

seq(coeff(series((1+4*x+3*x^2)/(1+3*x-x^3), x, n+1), x, n), n = 0..40); # G. C. Greubel, Oct 02 2019

Mathematica

Transpose[NestList[{#[[2]], Last[#], First[#]-3Last[#]}&, {1, 1, 0}, 35]][[1]]  (* Harvey P. Dale, Mar 13 2011 *)
LinearRecurrence[{-3, 0, 1}, {1, 1, 0}, 40] (* G. C. Greubel, Oct 02 2019 *)

Prog

(PARI) Vec((1+4*x+3*x^2)/(1+3*x-x^3)+O(x^40)) \\ Charles R Greathouse IV, Jan 17 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+4*x+3*x^2)/(1+3*x-x^3) )); // G. C. Greubel, Oct 02 2019
(Sage)
def A122099_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+4*x+3*x^2)/(1+3*x-x^3)).list()
A122099_list(40) # G. C. Greubel, Oct 02 2019
(GAP) a:=[1, 1, 0];; for n in [4..40] do a[n]:=-3*a[n-1]+a[n-3]; od; a; # G. C. Greubel, Oct 02 2019

Crossrefs

Cf. A122100.

Sequence in context: A244400 A052536 A122100 * A026165 A377099 A336742

Adjacent sequences: A122096 A122097 A122098 * A122100 A122101 A122102

Keyword

sign,easy,less

Author

Philippe Deléham, Oct 18 2006

Status

approved