%I
%S 0,0,1,1,4,8,25,62,176,470,1311,3620,10094,28209,79236,223270,631240,
%T 1790213,5090995,14515788,41484907,118821599,341008317,980487770,
%U 2823961866,8146372122,23534556225,68083326558,197209108054,571910949743,1660395053569,4825540091342
%N Number of primitive (period n) nbead bracelet structures which are not periodic palindromes using exactly three different colored beads.
%C Permuting the colors of the beads will not change the structure.
%H Andrew Howroyd, <a href="/A328038/b328038.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = A056367(n)  A056519(n).
%e For n = 3, the 1 bracelet structure has the pattern: ABC.
%e For n = 4, the 1 bracelet structure has the pattern: AABC.
%e For n = 5, the 4 bracelet structures have the patterns: AAABC, AABAC, AABBC, ABABC. The pattern ABBAC is excluded because it is a periodic palindrome.
%e For n = 6, the 8 bracelet structures have the patterns: ABCCCC, ABBCCC, ABBBCB, ABBCBC, ABBCCB, ABCBBC, AABBCC, AABCBC.
%Y Column 3 of A309784.
%Y Cf. A056367, A056519, A328035, A328039, A328657.
%K nonn
%O 1,5
%A _Andrew Howroyd_, Oct 02 2019
