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A261498 Number of necklaces with n white beads and 4*n black beads. 2
1, 1, 5, 31, 245, 2126, 19811, 192130, 1922741, 19692535, 205446630, 2175519380, 23322657491, 252631900236, 2760768051914, 30400169157656, 336977765092789, 3757141504436393, 42107201595510563, 474084628585822413, 5359833704140820870, 60823006052351729266 (list; graph; refs; listen; history; text; internal format)
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 * A276312 A024451 A046852

Adjacent sequences:  A261495 A261496 A261497 * A261499 A261500 A261501

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 21 2015

STATUS

approved

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)