A129903 Expansion of 1/(1+x^2-x^3+x^4).

1, 0, -1, 1, 0, -2, 2, 1, -4, 3, 3, -8, 4, 8, -15, 4, 19, -27, 0, 42, -46, -15, 88, -73, -57, 176, -104, -160, 337, -120, -393, 617, -64, -890, 1074, 209, -1900, 1755, 1035, -3864, 2620, 3144, -7519, 3340, 8043, -14003, 2816, 18706, -24862, -1887, 40752, -41681, -17777, 84320, -64656, -60416, 166753, -88560, -162513

Offset: 0

Author

Roger L. Bagula, Jun 04 2007

Keywords

• easy
• sign

Comments

Expansion of the characteristic polynomial of Jones polynomial for the Solomon knot (L4a1): f(x)=-1/Sqrt[x] + 1/x^{3/2} - 1/x^{5/2} - 1/x^{9/2};

Links

• Knot atlas, L4a1
• Index entries for linear recurrences with constant coefficients, signature (0,-1,1,-1).

Programs

Mathematica

f[q_] = -1/Sqrt[q] + 1/q^{3/2} - 1/q^{5/2} - 1/q^{9/2} FullSimplify[ExpandAll[f[q]/Sqrt[q]]]; g[q_] = 1 + q^2 - q^3 + q^4; q[x_] := 1/g[x]; Table[ SeriesCoefficient[Series[q[x], {x, 0, 30}], n], {n, 0, 30}]
LinearRecurrence[{0,-1,1,-1},{1,0,-1,1},70] (* Harvey P. Dale, Oct 27 2018 *)