A099447 - OEIS

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A099447

An Alexander sequence for the knot 6_3.

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 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The denominator is a parameterisation of the Alexander polynomial for the knot 6_3. 1/(1-3x+5x^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)).`
	LINKS	`Table of n, a(n) for n=0..31.` `Dror Bar-Natan, The Rolfsen Knot Table` `Index to sequences with linear recurrences with constant coefficients, signature (3,-5,3,-1).`
	FORMULA	`G.f.: (1-x)(1+x)(1+x^2)/(1-3x+5x^2-3x^3+x^4); - corrected Nov 24 2012` `a(n)=A099446(n)-A099446(n-2).`
	CROSSREFS	`Sequence in context: A213280 A056862 A113035 * A078067 A192442 A009126` `Adjacent sequences: A099444 A099445 A099446 * A099448 A099449 A099450`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry, Oct 16 2004`
	STATUS	`approved`

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Last modified May 18 18:13 EDT 2013. Contains 225422 sequences.