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A Chebyshev transform related to the knot 7_1.

+0
3

1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2, -1, -1, 0, 1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2, -1, -1, 0, 1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2, -1, -1, 0, 1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2, -1, -1, 0, 1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2, -1, -1, 0, 1, 1, 2, 2, 1, 1, 0, -1, -1, -2, -2 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`The g.f. is the transform of the g.f. of A006053(n+1) under the Chebyshev mapping G(x)-> (1/(1+x^2))G(x/(1+x^2)). The denominator of the g.f. is a paramaterisation of the Alexander polynomial of 7_1. It is also the 14th cyclotomic polynomial.`
	FORMULA	`G.f.: (1+x^2)^2/(1-x+x^2-x^3+x^4-x^5+x^6); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*A006053(n-2k+1)}.`
	CROSSREFS	`Cf. A099859.` `Adjacent sequences: A099857 A099858 A099859 this_sequence A099861 A099862 A099863` `Sequence in context: A087479 A039978 A099918 this_sequence A123736 A081389 A133685`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 28 2004`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.

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