Necklaces vs Bracelets

[Meeussen Wouter (bkarnd)]

ID Number: A047996
Sequence:  1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,3,4,3,1,1,1,1,
Name:      Triangle of circular binomial coefficients T(n,k), 0<=k<=n.
Comments:  T(n,k)=number of necklaces with k black beads, n-k white beads.
Formula : (1/n) * Sum_{d | (n,k)} phi(d)*binomial(n/d,k/d).



ID Number: A052307	
Sequence:  1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,3,3,3,1,1,1,1,	
           3,4,4,3,1,1,1,1,4,5,8,5,4,1,1,1,1,4,7,10,10,7,4,1,1,1,1,5,8,	
           16,16,16,8,5,1,1,1,1,5,10,20,26,26,20,10,5,1,1,1,1,6,12,29,	
           38,50,38,29,12,6,1,1,1,1,6	
Name:      Triangle: T(n,k): bracelets (reversible necklaces) with n black

              beads and n-k white beads.	
Formula : nihil !
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Author(s): Christian G. Bower (bowerc at usa.net), Nov 1999.

for even rows (=2n beads) and m=1..n this appears to be :
(1/2)*(C(2*(n\2),m\2) +Sum (d|(2n,m) phi(d)C(2n/d,m/d) ) - (-1)^n
if(even(n+m) ,0, C(n-1, floor(m/2-1/2) )	

who can give the formula for the complete A052307 ?

greets,

W.

Wouter Meeussen
email : wouter.meeussen at vandemoortele.com



===============================
This email is confidential and intended solely for the use of the individual to whom it is addressed. 
If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited.
You are explicitly requested to notify the sender of this email that the intended recipient was not reached.