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%I #12 Nov 01 2017 12:25:05
%S 1,4,13,60,291,1564,8671,49852,292927,1753964,10656757,65549844,
%T 407347747,2553684852,16130539053,102563204892,655918173287,
%U 4216358457772,27227967629683,176554882805940,1149099219084877,7504110622072860,49155856119036993,322903351882566436
%N Number of n-bead necklaces labeled with numbers -3..3 not allowing reversal, with sum zero.
%H Andrew Howroyd, <a href="/A208592/b208592.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A025012(d). - _Andrew Howroyd_, Mar 02 2017
%e All solutions for n=3:
%e .-2...-1...-3...-3...-1...-2...-3...-2...-3...-2...-2...-1....0
%e ..1....0....2....1....1....0....0....3....3...-1....2...-1....0
%e ..1....1....1....2....0....2....3...-1....0....3....0....2....0
%t 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_ *)
%Y Column 3 of A208597.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 29 2012
%E a(20)-a(24) from _Andrew Howroyd_, Mar 02 2017
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