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A099446 A Chebyshev transform of A057083. 1

%I #9 Sep 09 2015 01:29:02

%S 1,3,5,3,-8,-27,-37,-3,103,240,233,-189,-1115,-1941,-1048,3405,10747,

%T 14013,-433,-42528,-94127,-85053,88325,450387,748504,343605,-1448869,

%U -4269507,-5281865,811728,17484857,36819843,30752293

%N A Chebyshev transform of A057083.

%C 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)).

%H Dror Bar-Natan, <a href="http://katlas.org/wiki/Main_Page">The Rolfsen Knot Table</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,3,-1).

%F 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};

%K easy,sign

%O 0,2

%A _Paul Barry_, Oct 16 2004

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)