login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A099452
An Alexander sequence for the knot 7_7.
2
1, 5, 16, 40, 79, 110, 23, -520, -2336, -6995, -16574, -31075, -38848, 9560, 258631, 1043950, 2978719, 6781640, 12060848, 13119125, -12022526, -124662155, -461573264, -1259138680, -2752822273, -4615067410, -4134056729, 8360350360, 58685747584, 202130368445, 528415922498
OFFSET
0,2
COMMENTS
The denominator is a parameterization of the Alexander polynomial for the knot 7_7. 1/(1-5*x+9*x^2-5*x^3+x^4) is the image of the g.f. of A099450 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2)).
FORMULA
G.f.: (1-x)*(1+x)*(1+x^2)/(1-5*x+9*x^2-5*x^3+x^4). - corrected by R. J. Mathar, Nov 24 2012
a(n)=A099451(n)-A099451(n-2).
MATHEMATICA
LinearRecurrence[{5, -9, 5, -1}, {1, 5, 16, 40, 79}, 40] (* Harvey P. Dale, Apr 18 2019 *)
CROSSREFS
Sequence in context: A269747 A011863 A027085 * A006007 A001753 A202087
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 16 2004
STATUS
approved