A129704 Expansion of 1/(x^5 - 2*x^4 + x^3 - 2*x^2 + x - 1).

-1, -1, 1, 2, 1, -1, -4, -4, 3, 10, 7, -6, -20, -18, 12, 47, 39, -27, -100, -89, 53, 224, 202, -115, -490, -453, 232, 1080, 1028, -484, -2377, -2309, 985, 5222, 5213, -2005, -11488, -11724, 4043, 25226, 26387, -8062, -55420

Offset: 0

Author

Roger L. Bagula, Jun 01 2007

Keywords

• sign
• easy

Comments

The integer sequence is generated if the factor x^(3/2) is removed from the Jones polynomial of the Whitehead Link.

Links

• The Knot Atlas, L5a1
• Abhijit Champanerkar, Ilya Kofman and Eric Patterson, The next simplest hyperbolic knots, arXiv:math.GT/0311380, Table 2, page 14
• Eric Weisstein's World of Mathematics, Whitehead Link
• Index entries for linear recurrences with constant coefficients, signature (1,-2,1,-2,1).

Programs

Maple

A129704 := proc(n) coeftayl(1/(x^5-2*x^4+x^3-2*x^2+x-1),x=0,n) ; end proc: # R. J. Mathar, Sep 09 2011

Mathematica

q[x_] := 1/(x^5 - 2*x^4 + x^3 - 2*x^2 + x - 1) Table[ SeriesCoefficient[Series[q[x], {x, 0, 30}], n], {n, 0, 30}]

PARI

Vec(1/(x^5-2*x^4+x^3-2*x^2+x-1)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

G.f. 1/(x^5 - 2*x^4 + x^3 - 2*x^2 + x - 1).