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%I #11 Oct 07 2017 11:38:45
%S 1,3,4,0,-13,-30,-29,24,140,243,130,-429,-1348,-1752,67,5346,11795,
%T 10608,-11180,-56541,-93694,-42525,182452,535440,660179,-106782,
%U -2197373,-4613112,-3832996,5081235,22766722,36008115
%N An Alexander sequence for the knot 6_3.
%C The denominator is a parameterization of the Alexander polynomial for the knot 6_3. 1/(1-3*x+5*x^2-3*x^3+x^4) is the image of the g.f. of A057083 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 (3,-5,3,-1).
%F G.f.: (1-x)*(1+x)*(1+x^2)/(1-3x+5x^2-3x^3+x^4); - corrected Nov 24 2012
%F a(n)=A099446(n)-A099446(n-2).
%t LinearRecurrence[{3,-5,3,-1},{1,3,4,0,-13},40] (* _Harvey P. Dale_, Oct 07 2017 *)
%K easy,sign
%O 0,2
%A _Paul Barry_, Oct 16 2004