The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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