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

Author

Andrew Howroyd, Sep 12 2019

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Column k=3 of A309651.

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

Formula

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

Moebius transform of A305542.