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A099454 A Chebyshev transform of A099453 associated to the knot 8_12. 2
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; text; internal format)
OFFSET

0,2

COMMENTS

The denominator is a parameterization 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)).

LINKS

Table of n, a(n) for n=0..21.

Dror Bar-Natan, The Rolfsen Knot Table

Index entries for linear recurrences with constant coefficients, signature (7,-13,7,-1).

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}.

CROSSREFS

Sequence in context: A172063 A208737 A005061 * A177414 A125317 A006419

Adjacent sequences:  A099451 A099452 A099453 * A099455 A099456 A099457

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)