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 (1,6,24,8,-16,-64).
FORMULA
G.f.: (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)).
MAPLE
(1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3));
taylor(%, x=0, 10) ; # R. J. Mathar, Sep 09 2011
MATHEMATICA
p[x_, q_]= (1-q^2*x^2-q^3*x^3)/((1+q*x+q^2*x^2)*(1-x-q*x-q^2*x^2- q^2*x^3+q^4*x^4));
CoefficientList[Series[p[x, 2], {x, 0, 40}], x]
LinearRecurrence[{1, 6, 24, 8, -16, -64}, {1, 1, 3, 25, 75, 289}, 40] (* G. C. Greubel, Feb 06 2024 *)
PROG
(PARI) Vec((1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)) )); // G. C. Greubel, Feb 06 2024
(SageMath)
def A129443_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)) ).list()
A129443_list(40) # G. C. Greubel, Feb 06 2024
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Jun 08 2007
STATUS
approved