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A208592 Number of n-bead necklaces labeled with numbers -3..3 not allowing reversal, with sum zero. 2
1, 4, 13, 60, 291, 1564, 8671, 49852, 292927, 1753964, 10656757, 65549844, 407347747, 2553684852, 16130539053, 102563204892, 655918173287, 4216358457772, 27227967629683, 176554882805940, 1149099219084877, 7504110622072860, 49155856119036993, 322903351882566436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..100

FORMULA

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A025012(d). - Andrew Howroyd, Mar 02 2017

EXAMPLE

All solutions for n=3:

.-2...-1...-3...-3...-1...-2...-3...-2...-3...-2...-2...-1....0

..1....0....2....1....1....0....0....3....3...-1....2...-1....0

..1....1....1....2....0....2....3...-1....0....3....0....2....0

MATHEMATICA

comps[r_, m_, k_] := Sum[(-1)^i*Binomial[r - 1 - i*m, k - 1]*Binomial[k, i], {i, 0, Floor[(r - k)/m]}]; a[n_Integer, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] = a[n, 3]; Array[a, 24] (* Jean-Fran├žois Alcover, Nov 01 2017, after Andrew Howroyd *)

CROSSREFS

Column 3 of A208597.

Sequence in context: A149487 A320359 A057712 * A213093 A135312 A287145

Adjacent sequences:  A208589 A208590 A208591 * A208593 A208594 A208595

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 29 2012

EXTENSIONS

a(20)-a(24) from Andrew Howroyd, Mar 02 2017

STATUS

approved

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Last modified October 23 11:48 EDT 2019. Contains 328345 sequences. (Running on oeis4.)