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
KEYWORD
sign,easy,less
AUTHOR
Philippe Deléham, Oct 18 2006
STATUS
approved