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A129443
Expansion of (1 - 4*x^2 - 8*x^3)/((1 + 2*x + 4*x^2)*(1 - x - 2*x - 4*x^2 - 4*x^3 + 16*x^4)).
2
1, 1, 3, 25, 75, 289, 1283, 4905, 19547, 79281, 315123, 1260153, 5049419, 20180865, 80722531, 322959049, 1291700027, 5166801489, 20667742419, 82669888537, 330679592235, 1322722573857, 5290881765955, 21163527357033, 84654142731803
OFFSET
0,3
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
Cf. A129441.
Sequence in context: A242974 A006222 A290165 * A083298 A083222 A041565
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Jun 08 2007
STATUS
approved