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A261496
Number of necklaces with n white beads and n^2-n black beads.
2
1, 1, 2, 10, 116, 2126, 54132, 1753074, 69159400, 3220837534, 173103115760, 10551652603526, 719578430426044, 54297978110913252, 4492502634679508204, 404469190271900056316, 39370123445405248353744, 4120204305690280446004838, 461365717080849798202175772
OFFSET
0,3
LINKS
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
Eric Weisstein's World of Mathematics, Necklace
FORMULA
a(n) = 1/(n^2) * Sum_{d|n} C(n^2/d,n/d) * A000010(d) for n>0, a(0) = 1.
a(n) ~ exp(n-1/2) * n^(n-5/2) / sqrt(2*Pi). - Vaclav Kotesovec, Aug 22 2015
MAPLE
with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(n^2/d, n/d)
*phi(d), d=divisors(n))/n^2):
seq(a(n), n=0..20);
CROSSREFS
Lower diagonal of A261494.
Cf. A000010.
Sequence in context: A132522 A187653 A131811 * A347014 A356514 A006121
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 21 2015
STATUS
approved