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Search: id:A099448
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| A099448 |
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A Chebyshev transform of A030191 associated to the knot 7_6. |
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+0
2
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| 1, 5, 19, 65, 216, 715, 2369, 7855, 26051, 86400, 286549, 950345, 3151831, 10453085, 34667784, 114976135, 381319781, 1264651795, 4194233399, 13910227200, 46133441401, 153002131805, 507433471819, 1682909416265, 5581389996216
(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 7_6. The g.f. is the image of the g.f. of A030191 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)/(1-5x+7x^2-5x^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*5^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A030191(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A030191(k)/2}; a(n)=sum{k=0..n, A099449(n-k)*binomial(1, k/2)(1+(-1)^k)/2};
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CROSSREFS
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Sequence in context: A001870 A025568 A001047 this_sequence A124806 A059509 A137745
Adjacent sequences: A099445 A099446 A099447 this_sequence A099449 A099450 A099451
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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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