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

0,7

Links

Table of n, a(n) for n=0..56.

The Knot Atlas, L6a3

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

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

Mathematica

CoefficientList[Series[-1/(1 - x + x^2 - x^3 + x^4 + x^6), {x, 0, 50}], x]

Crossrefs

Cf. A008620, A010892, A014019, A099443, A099479, A099480, A112712, A129920, A129704, A129903.

Sequence in context: A165013 A351995 A055290 * A339160 A355755 A141335

Adjacent sequences: A125626 A125627 A125628 * A125630 A125631 A125632

Keyword

sign,easy

Author

Roger L. Bagula, Jun 07 2007

Extensions

Edited by Franck Maminirina Ramaharo, Jan 08 2019

Status

approved