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

1,5

Comments

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

Links

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

Formula

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

Example

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.

Crossrefs

Column 3 of A309784.

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

Sequence in context: A292548 A000964 A297458 * A107840 A046736 A174171

Adjacent sequences: A328035 A328036 A328037 * A328039 A328040 A328041

Keyword

nonn

Author

Andrew Howroyd, Oct 02 2019

Status

approved