A125629 Expansion of -1/(1 - x + x^2 - x^3 + x^4 + x^6).
1, -1, 0, 0, 0, 1, 2, 2, 1, 0, -1, -3, -5, -5, -3, 0, 4, 9, 13, 13, 8, -1, -13, -26, -35, -34, -20, 6, 40, 74, 95, 89, 48, -26, -120, -209, -258, -232, -111, 98, 355, 587, 699, 601, 245, -342, -1040, -1641, -1887, -1545, -504, 1137, 3023, 4568, 5073, 3936, 912
Offset: 0
Links
- The Knot Atlas, L6a3
- Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,0,-1).
Crossrefs
Programs
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Mathematica
CoefficientList[Series[-1/(1 - x + x^2 - x^3 + x^4 + x^6), {x, 0, 50}], x]
Formula
G.f.: 1/(x^(17/2)*f(x)), where f(x) = -1/x^(5/2) - 1/x^(9/2) + 1/x^(11/2) + -1/x^(13/2) + 1/x^(15/2) - 1/x^(17/2) is the Jones polynomial for the link with Dowker-Thistlethwaite notation L6a3.
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-6), n >= 6. - Franck Maminirina Ramaharo, Jan 08 2019
Extensions
Edited by Franck Maminirina Ramaharo, Jan 08 2019