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A099454
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A Chebyshev transform of A099453 associated to the knot 8_12.
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2
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1, 7, 37, 175, 792, 3521, 15539, 68369, 300431, 1319472, 5793745, 25437727, 111681277, 490315231, 2152620360, 9450575729, 41490490763, 182153978153, 799702876895, 3510901281888, 15413758929889, 67670362004791
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The denominator is a parameterisation of the Alexander polynomial for the knot 8_12. The g.f. is the image of the g.f. of A099453 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
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LINKS
| Dror Bar-Natan, The Rolfsen Knot Table
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FORMULA
| G.f.: (1+x^2)/(1-7x+13x^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)(-11)^j*7^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A099453(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A099453(k)/2}; a(n)=sum{k=0..n, A099455(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
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CROSSREFS
| Sequence in context: A169726 A172063 A005061 * A177414 A125317 A006419
Adjacent sequences: A099451 A099452 A099453 * A099455 A099456 A099457
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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