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Search: id:A099460
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| A099460 |
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A Chebyshev transform of A099459 associated to the knot 9_48. |
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+0
3
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| 1, 7, 39, 203, 1040, 5313, 27133, 138565, 707643, 3613904, 18456077, 94254531, 481354555, 2458260679, 12554250288, 64114111901, 327428500337, 1672165762785, 8539691368807, 43611901581472, 222724437852585
(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_48. The g.f. is the image of the g.f. of A099459 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
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LINKS
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The Rolfsen Knot Table
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FORMULA
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G.f.: (1+x^2)/(1-7x+11x^2-7x^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)(-9)^j*7^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*a099459(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A099459(k)/2}; a(n)=sum{k=0..n, A099461(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
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CROSSREFS
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Adjacent sequences: A099457 A099458 A099459 this_sequence A099461 A099462 A099463
Sequence in context: A026379 A026708 A016127 this_sequence A092923 A125786 A071082
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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