A326660 Number of n-bead asymmetric bracelets with exactly 3 different colored beads.

0, 0, 1, 3, 12, 34, 111, 315, 933, 2622, 7503, 21033, 59472, 167118, 472120, 1332945, 3777600, 10720869, 30516447, 87032994, 248820704, 712743768, 2045784183, 5882367570, 16942974048, 48876558318, 141204944529, 408494941773, 1183247473872, 3431450670601

Offset

1,4

Comments

Asymmetric bracelets are those primitive (period n) bracelets that when turned over are different from themselves.

Links

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

Formula

a(n) = A032240(n) - 3*A032239(n) for n >= 3.

Moebius transform of A305542.

Example

Case n = 4: There are 3 distinct asymmetric bracelets with exactly 3 colors which are aabc, abbc, abcc.

Crossrefs

Column k=3 of A309651.

Cf. A032239, A032240, A056343, A056349, A305542, A326789.

Sequence in context: A073372 A305023 A026573 * A225075 A293267 A295363

Adjacent sequences: A326657 A326658 A326659 * A326661 A326662 A326663

Keyword

nonn

Author

Andrew Howroyd, Sep 12 2019

Status

approved