A099859 - OEIS

A099859

A Chebyshev transform of A006053 related to the knot 7_1.

0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1

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OFFSET

0,1

COMMENTS

The g.f. is the transform of the g.f. of A006053 under the Chebyshev mapping G(x)-> (1/(1+x^2))G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial of 7_1. It is also the 14th cyclotomic polynomial.

LINKS

Table of n, a(n) for n=0..81.

FORMULA

G.f.: x(1+x^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)}.

CROSSREFS

Cf. A099860.

Sequence in context: A161382 A138886 A269528 * A176416 A102460 A080908

Adjacent sequences: A099856 A099857 A099858 * A099860 A099861 A099862

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 28 2004

STATUS

approved