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Search: id:A099457
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| A099457 |
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A Chebyshev transform of A099456 associated to the knot 9_44. |
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+0
3
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| 1, 4, 10, 16, 9, -40, -169, -376, -490, 36, 2239, 7120, 13441, 12844, -16470, -109144, -283351, -448120, -229129, 1196064, 4879030, 10675276, 13561279, -2161760, -65753919, -204313516, -379184950, -347399104, 513198089
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The denominator is a parameterisation of the Alexander polynomial for the knot 9_44. The g.f. is the image of the g.f. of A099456 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
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LINKS
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Dror Bar-Natan, The Rolfsen Knot Table
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FORMULA
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G.f.: (1+x^2)/(1-4x+7x^2-4x^3+x^4); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(n-2k-j, j)(-5)^j*4^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A099456(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A099456(k)/2}; a(n)=sum{k=0..n, A099458(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
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CROSSREFS
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Sequence in context: A122782 A153515 A005662 this_sequence A055103 A030332 A119409
Adjacent sequences: A099454 A099455 A099456 this_sequence A099458 A099459 A099460
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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