

A328038


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


4



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
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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



