A056304 Number of primitive (period n) n-bead necklace structures using exactly three different colored beads.

0, 0, 1, 2, 5, 17, 43, 124, 338, 941, 2591, 7234, 20125, 56407, 158349, 446492, 1262225, 3580330, 10181479, 29031306, 82968799, 237642659, 682014587, 1960974220, 5647919640, 16292741605, 47069104274, 136166647110, 394418199725, 1143821887473, 3320790074371

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

Comments

Turning over the necklace is not allowed. Colors may be permuted without changing the necklace structure.

References

• M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Column 3 of A107424.

Cf. A000048, A002075, A008683, A056288, A056296.

Formula

a(n) = Sum_{d|n} mu(d)*A056296(n/d), where mu = A008683 is the Möbius function.

a(n) = A002075(n) - A000048(n).

Extensions

a(28)-a(31) from Pontus von Brömssen, Aug 04 2024