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A099844 An Alexander sequence for the knot 8_2. 1
1, 3, 6, 12, 24, 48, 98, 201, 411, 840, 1716, 3504, 7156, 14616, 29853, 60975, 124542, 254376, 519560, 1061196, 2167482, 4427061, 9042231, 18468672, 37722088, 77047008, 157367784, 321422208, 656501817, 1340898747, 2738772998 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The g.f. is a transformation of the g.f. 1/(1-3x+3x^3) of A090400 under the mapping G(x)->(1/(1+x^2)^3)G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial for the knot 8_2.

LINKS

Table of n, a(n) for n=0..30.

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

FORMULA

G.f.: 1/(1-3x+3x^2-3x^3+3x^4-3x^5+x^6).

MATHEMATICA

LinearRecurrence[{3, -3, 3, -3, 3, -1}, {1, 3, 6, 12, 24, 48}, 40] (* Harvey P. Dale, Sep 18 2019 *)

CROSSREFS

Cf. A099845.

Sequence in context: A007283 A049942 A200463 * A165929 A084717 A102254

Adjacent sequences:  A099841 A099842 A099843 * A099845 A099846 A099847

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 27 2004

STATUS

approved

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Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)