A261499 Number of necklaces with n white beads and 5*n black beads.

1, 1, 6, 46, 446, 4751, 54132, 642342, 7861662, 98480332, 1256569506, 16273981758, 213378976004, 2826867619109, 37782553160820, 508840821830546, 6898459216311582, 94070535317459018, 1289430373206452136, 17755914760643605782, 245518560760433583946

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..850

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/(6*n) * Sum_{d|n} C(6*n/d,n/d) * A000010(d) for n>0, a(0) = 1.

a(n) ~ 6^(6*n) / (2 * sqrt(3*Pi) * 5^(5*n+1/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(6*n/d, n/d)
             *phi(d), d=divisors(n))/(6*n)):
seq(a(n), n=0..25);

Crossrefs

Column k=5 of A261494.

Sequence in context: A049378 A365056 A218497 * A001829 A006386 A326324

Adjacent sequences: A261496 A261497 A261498 * A261500 A261501 A261502

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved