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A261502 Number of necklaces with n white beads and 8*n black beads. 2
1, 1, 9, 109, 1641, 27151, 478341, 8782075, 166237161, 3220837534, 63562741159, 1273237637706, 25820645555109, 529080420540114, 10937268142896643, 227824992158991334, 4777204094770874857, 100757627271124231383, 2136117417348870713646, 45496022230420668679932 (list; graph; refs; listen; history; text; internal format)
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: A199030 A288692 A291815 * A105974 A053912 A053894

Adjacent sequences:  A261499 A261500 A261501 * A261503 A261504 A261505

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 21 2015

STATUS

approved

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Last modified September 20 18:29 EDT 2021. Contains 347588 sequences. (Running on oeis4.)