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

0, 0, 1, 1, 4, 8, 25, 62, 176, 470, 1311, 3620, 10094, 28209, 79236, 223270, 631240, 1790213, 5090995, 14515788, 41484907, 118821599, 341008317, 980487770, 2823961866, 8146372122, 23534556225, 68083326558, 197209108054, 571910949743, 1660395053569, 4825540091342

Offset: 1

Author

Andrew Howroyd, Oct 02 2019

Keywords

• nonn

Comments

Permuting the colors of the beads will not change the structure.

Examples

			For n = 3, the 1 bracelet structure has the pattern: ABC.
For n = 4, the 1 bracelet structure has the pattern: AABC.
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.
For n = 6, the 8 bracelet structures have the patterns: ABCCCC, ABBCCC, ABBBCB, ABBCBC, ABBCCB, ABCBBC, AABBCC, AABCBC.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Column 3 of A309784.

Cf. A056367, A056519, A328035, A328039, A328657.

Formula

a(n) = A056367(n) - A056519(n).