A099446 A Chebyshev transform of A057083.

1, 3, 5, 3, -8, -27, -37, -3, 103, 240, 233, -189, -1115, -1941, -1048, 3405, 10747, 14013, -433, -42528, -94127, -85053, 88325, 450387, 748504, 343605, -1448869, -4269507, -5281865, 811728, 17484857, 36819843, 30752293

Offset

0,2

Comments

The denominator is a parameterization of the Alexander polynomial for the knot 6_3. The g.f. is the image of the g.f. of A057083 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).

Links

Table of n, a(n) for n=0..32.

Dror Bar-Natan, The Rolfsen Knot Table

Index entries for linear recurrences with constant coefficients, signature (3,-5,3,-1).

Formula

G.f.: (1+x^2)/(1-3x+5x^2-3x^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)(-3)^j*3^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A057083(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A057083(k)/2}; a(n)=sum{k=0..n, A099447(n-k)*binomial(1, k/2)(1+(-1)^k)/2};

Crossrefs

Sequence in context: A100338 A094444 A231641 * A198827 A199668 A318377

Adjacent sequences: A099443 A099444 A099445 * A099447 A099448 A099449

Keyword

easy,sign

Author

Paul Barry, Oct 16 2004

Status

approved