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A122100 a(n) = 3*a(n-1) - a(n-3) for n>2, with a(0)=1, a(1)=-1, a(2)=0. 7
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 (list; graph; refs; listen; history; text; internal format)
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).

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

LinearRecurrence[{3, 0, -1}, {1, -1, 0}, 40] (* Harvey P. Dale, Nov 14 2014 *)

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 A122100_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1-4*x+3*x^2)/(1-3*x+x^3)).list()

A122100_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. A052536.

Sequence in context: A299162 A244400 A052536 * A122099 A026165 A148445

Adjacent sequences:  A122097 A122098 A122099 * A122101 A122102 A122103

KEYWORD

sign,easy,less

AUTHOR

Philippe Deléham, Oct 18 2006

STATUS

approved

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Last modified November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)