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A099845 A Chebyshev transform of A090400 related to the knot 8_2. 1
1, 3, 8, 18, 37, 75, 152, 309, 631, 1290, 2636, 5385, 10999, 22464, 45881, 93711, 191404, 390942, 798497, 1630923, 3331144, 6803829, 13896755, 28383990, 57974032, 118411413, 241854191, 493984896, 1008959473, 2060790171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The g.f. is a transformation of the g.f. 1/(1-3x+3x^3) of A090400 under the Chebyshev transform G(x)->(1/(1+x^2))G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial for the knot 8_2.

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-3,3,-1).

FORMULA

G.f.: (1+x^2)^2/(1-3x+3x^2-3x^3+3x^4-3x^5+x^6); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*A090400(n-2k)}; a(n)=sum{k=0..n, A099844(n-k)*binomial(2, k/2)(1+(-1)^k)/2}.

CROSSREFS

Sequence in context: A241080 A000234 A136376 * A036635 A000713 A261325

Adjacent sequences:  A099842 A099843 A099844 * A099846 A099847 A099848

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 27 2004

STATUS

approved

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Last modified November 12 09:24 EST 2019. Contains 329052 sequences. (Running on oeis4.)