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

1,5

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

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

Example

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.

Crossrefs

Cf. A056362, A056514, A309784, A328038.

Sequence in context: A020181 A216134 A226908 * A335983 A113682 A291064

Adjacent sequences: A328654 A328655 A328656 * A328658 A328659 A328660

Keyword

nonn

Author

Andrew Howroyd, Oct 24 2019

Status

approved