A261503 Number of necklaces with n white beads and 9*n black beads.

1, 1, 10, 136, 2290, 42376, 834472, 17125354, 362345362, 7847250409, 173103115760, 3875837737520, 87857163416200, 2012268157890524, 46497242510288804, 1082614775186919136, 25374686712458407442, 598217593341171422090, 14176230568954212214234

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..710

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

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]

Eric Weisstein's World of Mathematics, Necklace

Wikipedia, Necklace (combinatorics)

Index entries for sequences related to necklaces

Formula

a(n) = 1/(10*n) * Sum_{d|n} C(10*n/d,n/d) * A000010(d) for n>0, a(0) = 1.

a(n) ~ 10^(10*n-1/2) / (sqrt(2*Pi) * 9^(9*n+1/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(10*n/d, n/d)
             *phi(d), d=divisors(n))/(10*n)):
seq(a(n), n=0..25);

Crossrefs

Column k=9 of A261494.

Sequence in context: A065024 A026244 A371405 * A096619 A276131 A003377

Adjacent sequences: A261500 A261501 A261502 * A261504 A261505 A261506

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved