OFFSET
1,1
COMMENTS
Turning over will not create a new bracelet.
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
FORMULA
sum mu(d)*A056341(n/d) where d|n.
From Herbert Kociemba, Nov 28 2016: (Start)
More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.
gf(k): Sum_{n>=1} mu(n)*( -log(1-k*x^n)/n + Sum_{i=0..2} binomial(k,i)x^(n*i)/(1-k*x^(2*n)) )/2. (End)
MATHEMATICA
mx=40; gf[x_, k_]:=Sum[ MoebiusMu[n]*(-Log[1-k*x^n]/n+Sum[Binomial[k, i]x^(n i), {i, 0, 2}]/( 1-k x^(2n)))/2, {n, mx}]; CoefficientList[Series[gf[x, 6], {x, 0, mx}], x] (* Herbert Kociemba, Nov 28 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved