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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
OFFSET
1,2
LINKS
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-François Alcover, Nov 01 2017, after Andrew Howroyd *)
CROSSREFS
Column 3 of A208597.
Sequence in context: A372125 A320359 A057712 * A367888 A351933 A356029
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 29 2012
EXTENSIONS
a(20)-a(24) from Andrew Howroyd, Mar 02 2017
STATUS
approved