OFFSET
0,2
COMMENTS
The denominator is a parameterization of the Alexander polynomial for the knot 7_7. The g.f. is the image of the g.f. of A099450 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
LINKS
Dror Bar-Natan, The Rolfsen Knot Table
Index entries for linear recurrences with constant coefficients, signature (5,-9,5,-1).
FORMULA
G.f.: (1+x^2)/(1-5x+9x^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)*(-7)^j*5^(n-2k-2j).
a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*(-1)^k*A099450(n-2k).
a(n) = Sum_{k=0..n} binomial((n+k)/2, k)*(-1)^((n-k)/2)*(1+(-1)^(n+k))*A099450(k)/2.
a(n) = Sum_{k even, 0<=k<=n} A099452(n-k). [corrected by Kevin Ryde, Jul 24 2022]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 16 2004
STATUS
approved