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A099454 A Chebyshev transform of A099453 associated to the knot 8_12. 2


%S 1,7,37,175,792,3521,15539,68369,300431,1319472,5793745,25437727,

%T 111681277,490315231,2152620360,9450575729,41490490763,182153978153,

%U 799702876895,3510901281888,15413758929889,67670362004791

%N A Chebyshev transform of A099453 associated to the knot 8_12.

%C The denominator is a parameterization 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)).

%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 (7,-13,7,-1).

%F 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}.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 16 2004

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Last modified August 2 08:47 EDT 2021. Contains 346422 sequences. (Running on oeis4.)