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A099844
An Alexander sequence for the knot 8_2.
2
1, 3, 6, 12, 24, 48, 98, 201, 411, 840, 1716, 3504, 7156, 14616, 29853, 60975, 124542, 254376, 519560, 1061196, 2167482, 4427061, 9042231, 18468672, 37722088, 77047008, 157367784, 321422208, 656501817, 1340898747, 2738772998
OFFSET
0,2
COMMENTS
The g.f. is a transformation of the g.f. 1/(1-3*x+3*x^3) of A090400 under the mapping G(x) -> (1/(1+x^2)^3)*G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial for the knot 8_2.
FORMULA
G.f.: 1/(1 - 3*x + 3*x^2 - 3*x^3 + 3*x^4 - 3*x^5 + x^6).
MATHEMATICA
LinearRecurrence[{3, -3, 3, -3, 3, -1}, {1, 3, 6, 12, 24, 48}, 40] (* Harvey P. Dale, Sep 18 2019 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-3*x+3*x^2-3*x^3+3*x^4-3*x^5+x^6) )); // G. C. Greubel, Apr 20 2023
(SageMath)
def A077952_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-3*x+3*x^2-3*x^3+3*x^4-3*x^5+x^6) ).list()
A077952_list(40) # G. C. Greubel, Apr 20 2023
CROSSREFS
Sequence in context: A007283 A049942 A200463 * A165929 A084717 A102254
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 27 2004
STATUS
approved