11,3

The g.f. is Z(C_11,x)/x^11, the 11-variate cycle index polynomial for the cyclic group C_11, with substitution x[i]->1/(1-x^i), i=1,...,11. By Polya enumeration, a(n+11) is the number of cyclically inequivalent 11-necklaces whose 11 beads are labeled with nonnegative integers such that the sum of labels is n, for n=0,1,2,... See A102190 for Z(C_11,x). See the comment in A032191 on the equivalence of this problem with the one given in the `Name' line. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 15 2005.

C. G. Bower, Transforms (2)

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

Index entries for sequences related to necklaces

"CIK[ 11 ]" (necklace, indistinct, unlabeled, 11 parts) transform of 1, 1, 1, 1...

G.f.:(x^11)*(1-9*x+41*x^2-109*x^3+191*x^4-229*x^5+191*x^6-109*x^7+41*x^8-9*x^9+x^10 )/((1-x)^10*(1-x^11)).

a(n)=ceiling(binomial(n+11, 11)/(n+11)) (conjecture W. Lang).

k = 11; Table[Apply[Plus, Map[EulerPhi[ # ]Binomial[n/#, k/# ] &, Divisors[GCD[n, k]]]]/n, {n, k, 30}] - Robert A. Russell (russell(AT)post.harvard.edu), Sep 27 2004

Cf. A004526, A007997, A008610, A008646, A032191, A032192-A032195.

Sequence in context: A036422 A166214 A032169 this_sequence A011780 A036631 A036638

Adjacent sequences: A032193 A032194 A032195 this_sequence A032197 A032198 A032199

nonn

Christian G. Bower (bowerc(AT)usa.net)