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A328038 Number of primitive (period n) n-bead bracelet structures which are not periodic palindromes using exactly three different colored beads. 4

%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) n-bead 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

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Last modified September 24 11:31 EDT 2020. Contains 337318 sequences. (Running on oeis4.)