A261502 Number of necklaces with n white beads and 8*n black beads.

1, 1, 9, 109, 1641, 27151, 478341, 8782075, 166237161, 3220837534, 63562741159, 1273237637706, 25820645555109, 529080420540114, 10937268142896643, 227824992158991334, 4777204094770874857, 100757627271124231383, 2136117417348870713646, 45496022230420668679932

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..730

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/(9*n) * Sum_{d|n} C(9*n/d,n/d) * A000010(d) for n>0, a(0) = 1.

a(n) ~ 9^(9*n-1/2) / (sqrt(2*Pi) * 8^(8*n+1/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(9*n/d, n/d)
             *phi(d), d=divisors(n))/(9*n)):
seq(a(n), n=0..25);

Crossrefs

Column k=8 of A261494.

Sequence in context: A358601 A349335 A291815 * A359731 A105974 A053912

Adjacent sequences: A261499 A261500 A261501 * A261503 A261504 A261505

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved