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A099455 An Alexander sequence for the knot 8_12. 2


%S 1,7,36,168,755,3346,14747,64848,284892,1251103,5493314,24118255,

%T 105887532,464877504,2040939083,8960260498,39337870403,172703402424,

%U 758212386132,3328747303735,14614056052994,64159460722903

%N An Alexander sequence for the knot 8_12.

%C 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)).

%H Dror Bar-Natan, <a href="http://katlas.org/wiki/Main_Page">The Rolfsen Knot Table</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-13,7,-1).

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

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

%t LinearRecurrence[{7,-13,7,-1},{1,7,36,168,755},30] (* _Harvey P. Dale_, Jan 31 2017 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 16 2004

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Last modified June 20 17:31 EDT 2021. Contains 345189 sequences. (Running on oeis4.)