A129920 Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).

-1, -1, 2, 3, -4, -10, 5, 29, 2, -76, -45, 178, 212, -361, -750, 565, 2282, -306, -6206, -2428, 15176, 14353, -32719, -55104, 57933, 176234, -61524, -499047, -97429, 1271400, 921652, -2887641, -3948938, 5590078, 13380187, -7828378, -39536779, 108416, 104810904

Offset

0,3

Links

Table of n, a(n) for n=0..38.

The Knot Atlas, L6a1

Index entries for linear recurrences with constant coefficients, signature (1,-3,2,-1,2,-1).

Formula

G.f.: 1/(x^(9/2)*f(x)), where f(x) = -x^(3/2) + 2*x^(1/2) - 1/x^(1/2) + 2/x^(3/2) - 3/x^(5/2) + 1/x^(7/2) - 1/x^(9/2) is the Jones Polynomial for the link with Dowker-Thistlethwaite notation L6a1.

a(n) = a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6), n >= 6. - Franck Maminirina Ramaharo, Jan 08 2019

Mathematica

CoefficientList[Series[-1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6), {x, 0, 50}], x]

Crossrefs

Cf. A008620, A010892, A014019, A099443, A099479, A099480, A125629, A112712, A129704, A129903.

Sequence in context: A255479 A256618 A140598 * A356332 A065634 A364223

Adjacent sequences: A129917 A129918 A129919 * A129921 A129922 A129923

Keyword

sign,easy

Author

Roger L. Bagula, Jun 05 2007

Extensions

Edited by Franck Maminirina Ramaharo, Jan 08 2019

Status

approved