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A056347 Number of primitive (period n) bracelets using a maximum of six different colored beads. 2
6, 15, 50, 210, 882, 4220, 20640, 107100, 563730, 3036411, 16514100, 90778485, 502474350, 2799199380, 15673672238, 88162569180, 497847963690, 2821127257950, 16035812864940, 91404065292036 (list; graph; refs; listen; history; text; internal format)
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]

LINKS

Table of n, a(n) for n=1..20.

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

Column 6 of A276550.

Cf. A032164.

Sequence in context: A318414 A106272 A056423 * A271332 A244024 A122365

Adjacent sequences:  A056344 A056345 A056346 * A056348 A056349 A056350

KEYWORD

nonn

AUTHOR

Marks R. Nester

STATUS

approved

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Last modified August 11 19:16 EDT 2020. Contains 336428 sequences. (Running on oeis4.)