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A261501
Number of necklaces with n white beads and 7*n black beads.
3
1, 1, 8, 85, 1128, 16451, 255704, 4141383, 69159400, 1182125128, 20581159608, 363704640476, 6506965279992, 117626432708864, 2145180358634664, 39421026305282660, 729242353169440744, 13568988503585900648, 253785064586356459616, 4768543107831461199897
OFFSET
0,3
LINKS
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
Eric Weisstein's World of Mathematics, Necklace
FORMULA
a(n) = 1/(8*n) * Sum_{d|n} C(8*n/d,n/d) * A000010(d) for n>0, a(0) = 1.
a(n) ~ 2^(24*n-2) / (sqrt(Pi) * 7^(7*n+1/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015
MAPLE
with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(8*n/d, n/d)
*phi(d), d=divisors(n))/(8*n)):
seq(a(n), n=0..25);
CROSSREFS
Column k=7 of A261494.
Sequence in context: A300675 A241323 A349334 * A371897 A180582 A230621
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 21 2015
STATUS
approved