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A099458 An Alexander sequence for the knot 9_44. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..28.

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).

CROSSREFS

Sequence in context: A002641 A085724 A106854 * A069219 A312848 A010413

Adjacent sequences:  A099455 A099456 A099457 * A099459 A099460 A099461

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified May 30 08:43 EDT 2020. Contains 334712 sequences. (Running on oeis4.)