A099455 An Alexander sequence for the knot 8_12.

1, 7, 36, 168, 755, 3346, 14747, 64848, 284892, 1251103, 5493314, 24118255, 105887532, 464877504, 2040939083, 8960260498, 39337870403, 172703402424, 758212386132, 3328747303735, 14614056052994, 64159460722903

Offset

0,2

Comments

The denominator is a parameterization of the Alexander polynomial for the knot 8_12. 1/(1-7*x+13*x^2-7*x^3+x^4) is the image of the g.f. of A099453 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2)).

Links

Table of n, a(n) for n=0..21.

Dror Bar-Natan, The Rolfsen Knot Table

Index entries for linear recurrences with constant coefficients, signature (7,-13,7,-1).

Formula

G.f.: (1-x)(1+x)*(1+x^2)/(1-7x+13x^2-7x^3+x^4); - corrected Nov 24 2012

a(n)=A099454(n)-A099454(n-2).

Mathematica

LinearRecurrence[{7, -13, 7, -1}, {1, 7, 36, 168, 755}, 30] (* Harvey P. Dale, Jan 31 2017 *)

Crossrefs

Sequence in context: A292486 A026856 A038748 * A102053 A058681 A246417

Adjacent sequences: A099452 A099453 A099454 * A099456 A099457 A099458

Keyword

easy,nonn

Author

Paul Barry, Oct 16 2004

Status

approved