A261498 Number of necklaces with n white beads and 4*n black beads.

1, 1, 5, 31, 245, 2126, 19811, 192130, 1922741, 19692535, 205446630, 2175519380, 23322657491, 252631900236, 2760768051914, 30400169157656, 336977765092789, 3757141504436393, 42107201595510563, 474084628585822413, 5359833704140820870, 60823006052351729266

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..920

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/(5*n) * Sum_{d|n} C(5*n/d,n/d) * A000010(d) for n>0, a(0) = 1.

a(n) ~ 5^(5*n-1/2) / (sqrt(Pi) * 2^(8*n+3/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(5*n/d, n/d)
             *phi(d), d=divisors(n))/(5*n)):
seq(a(n), n=0..25);

Crossrefs

Column k=4 of A261494.

Sequence in context: A331335 A082579 A294214 * A368320 A276312 A024451

Adjacent sequences: A261495 A261496 A261497 * A261499 A261500 A261501

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved