A328657 Number of primitive (period n) n-bead bracelet structures which are not periodic palindromes using a maximum of three different colored beads.

0, 0, 1, 1, 4, 9, 26, 66, 183, 488, 1342, 3690, 10220, 28470, 79720, 224230, 633040, 1793727, 5097638, 14528640, 41509364, 118868750, 341098474, 980661510, 2824295364, 8147015352, 23535794889, 68085719208, 197213728060, 571919889400, 1660412355602, 4825573629390

Offset: 1

Author

Andrew Howroyd, Oct 24 2019

Keywords

• nonn

Comments

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

Examples

			For n <= 5, the structures are the same as in A328038.
For n = 6, the 9 bracelet structures have the patterns: AABABB, ABCCCC, ABBCCC, ABBBCB, ABBCBC, ABBCCB, ABCBBC, AABBCC, AABCBC.
		

Links

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

Crossrefs

Cf. A056362, A056514, A309784, A328038.

Formula

a(n) = Sum_{k=1..3} A309784(n, k).

a(n) = A056362(n) - A056514(n).