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A099447
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An Alexander sequence for the knot 6_3.
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1
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1, 3, 4, 0, -13, -30, -29, 24, 140, 243, 130, -429, -1348, -1752, 67, 5346, 11795, 10608, -11180, -56541, -93694, -42525, 182452, 535440, 660179, -106782, -2197373, -4613112, -3832996, 5081235, 22766722, 36008115
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OFFSET
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0,2
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COMMENTS
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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)).
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LINKS
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FORMULA
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G.f.: (1-x)*(1+x)*(1+x^2)/(1-3x+5x^2-3x^3+x^4); - corrected Nov 24 2012
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MATHEMATICA
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LinearRecurrence[{3, -5, 3, -1}, {1, 3, 4, 0, -13}, 40] (* Harvey P. Dale, Oct 07 2017 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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