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%I #12 Nov 01 2017 12:24:56
%S 1,3,7,23,77,297,1163,4783,20041,85735,371955,1634429,7254547,
%T 32486709,146576693,665720447,3041096613,13963651875,64410421307,
%U 298331882891,1386933722321,6469566027565,30271114380919,142037330038069,668187211909327
%N Number of n-bead necklaces labeled with numbers -2..2 not allowing reversal, with sum zero.
%H Andrew Howroyd, <a href="/A208591/b208591.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A005191(d). - _Andrew Howroyd_, Mar 02 2017
%e All solutions for n=3:
%e .-2...-1...-2...-2....0...-1...-1
%e ..2...-1....1....0....0....1....0
%e ..0....2....1....2....0....0....1
%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, 2]; Array[a, 25] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%Y Column 2 of A208597.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 29 2012
%E a(22)-a(25) from _Andrew Howroyd_, Mar 02 2017
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