|
Search: id:A099454
|
|
|
| A099454 |
|
A Chebyshev transform of A099453 associated to the knot 8_12. |
|
+0
3
|
|
| 1, 7, 37, 175, 792, 3521, 15539, 68369, 300431, 1319472, 5793745, 25437727, 111681277, 490315231, 2152620360, 9450575729, 41490490763, 182153978153, 799702876895, 3510901281888, 15413758929889, 67670362004791
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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)).
|
|
LINKS
|
Dror Bar-Natan, The Rolfsen Knot Table
|
|
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: A049494 A049495 A005061 this_sequence A125317 A006419 A026673
Adjacent sequences: A099451 A099452 A099453 this_sequence A099455 A099456 A099457
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
|
|
|
Search completed in 0.002 seconds
|
