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 A099860 A Chebyshev transform related to the knot 7_1. 2
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1). 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)}. MATHEMATICA LinearRecurrence[{1, -1, 1, -1, 1, -1}, {1, 1, 2, 2, 1, 1}, 100] (* Harvey P. Dale, May 21 2019 *) CROSSREFS Cf. A099859. Sequence in context: A285194 A039978 A099918 * A317950 A255212 A323011 Adjacent sequences:  A099857 A099858 A099859 * A099861 A099862 A099863 KEYWORD easy,sign AUTHOR Paul Barry, Oct 28 2004 STATUS approved

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)