A099458 An Alexander sequence for the knot 9_44.

1, 4, 9, 12, -1, -56, -178, -336, -321, 412, 2729, 7084, 11202, 5724, -29911, -121988, -266881, -338976, 54222, 1644184, 5108159, 9479212, 8682249, -12837036, -79315198, -202151756, -313431031, -143085588, 892383039

Offset: 0

Author

Paul Barry, Oct 16 2004

Keywords

• easy
• sign

Comments

The denominator 1-4x+7x^2-4x^3+x^4 is a parameterization of the Alexander polynomial for the knot 9_44. 1/(1-4x+7x^2-4x^3+x^4) is the image of the g.f. of A099456 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2)).

Links

• Dror Bar-Natan, The knot 9_44 in the Rolfsen Knot Table at the Knot Atlas

Formula

G.f.: (1-x)*(1+x)*(1+x^2)/(1-4*x+7*x^2-4*x^3+x^4); a(n)=A099457(n)-A099457(n-2).