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A099457 A Chebyshev transform of A099456 associated to the knot 9_44. 2
1, 4, 10, 16, 9, -40, -169, -376, -490, 36, 2239, 7120, 13441, 12844, -16470, -109144, -283351, -448120, -229129, 1196064, 4879030, 10675276, 13561279, -2161760, -65753919, -204313516, -379184950, -347399104, 513198089 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The denominator is a parameterization of the Alexander polynomial for the knot 9_44. The g.f. is the image of the g.f. of A099456 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).

LINKS

Table of n, a(n) for n=0..28.

Dror Bar-Natan, The Rolfsen Knot Table

Index entries for linear recurrences with constant coefficients, signature (4,-7,4,-1).

FORMULA

G.f.: (1+x^2)/(1-4x+7x^2-4x^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)(-5)^j*4^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A099456(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A099456(k)/2}; a(n)=sum{k=0..n, A099458(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.

CROSSREFS

Sequence in context: A218211 A302197 A190965 * A055103 A285629 A030332

Adjacent sequences:  A099454 A099455 A099456 * A099458 A099459 A099460

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified June 20 20:59 EDT 2021. Contains 345235 sequences. (Running on oeis4.)