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A099845
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A Chebyshev transform of A090400 related to the knot 8_2.
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1
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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; internal format)
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OFFSET
| 0,2
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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 parameterisation of the Alexander polynomial for the knot 8_2.
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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}.
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CROSSREFS
| Sequence in context: A169763 A000234 A136376 * A036635 A000713 A078409
Adjacent sequences: A099842 A099843 A099844 * A099846 A099847 A099848
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 27 2004
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