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A056291
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Number of primitive (period n) n-bead necklaces with exactly six different colored beads.
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4
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0, 0, 0, 0, 0, 120, 2160, 23940, 211680, 1643544, 11748240, 79419060, 516257280, 3262440960, 20193277104, 123071683140, 741419995680, 4427489935680, 26264144909520, 155018839412052, 911509010152560, 5344538372696880, 31272099902089200, 182707081042818360
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OFFSET
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1,6
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COMMENTS
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Turning over the necklace is not allowed.
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REFERENCES
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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]
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LINKS
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FORMULA
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MAPLE
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with(numtheory):
b:= proc(n, k) option remember; `if`(n=0, 1,
add(mobius(n/d)*k^d, d=divisors(n))/n)
end:
a:= n-> add(b(n, 6-j)*binomial(6, j)*(-1)^j, j=0..6):
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n==0, 1, DivisorSum[n, MoebiusMu[n/#]*k^# &]/n];
a[n_] := Sum[b[n, 6 - j]*Binomial[6, j]*(-1)^j, {j, 0, 6}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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