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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-3,3,-1).
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 27 2004
STATUS
approved