A056362 Number of primitive (period n) bracelet structures using a maximum of three different colored beads.

1, 1, 1, 2, 4, 8, 18, 39, 94, 222, 572, 1463, 3934, 10584, 29211, 80808, 226430, 636320, 1800318, 5107479, 14548360, 41538874, 118927919, 341187047, 980838750, 2824561080, 8147547156, 23536592010, 68087313892, 197216119544, 571924673368, 1660419530055, 4825587979390

Offset

0,4

Comments

Turning over will not create a new bracelet. Permuting the colors of the beads will not change the 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]

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{d|n} mu(d)*A056353(n/d) for n > 0.

a(n) = Sum_{k=1..3} A276543(n, k) for n > 0. - Andrew Howroyd, Oct 26 2019

Crossrefs

Cf. A002075, A056353, A056367, A276543.

Sequence in context: A300221 A233437 A321200 * A086585 A329971 A052910

Adjacent sequences: A056359 A056360 A056361 * A056363 A056364 A056365

Keyword

nonn

Author

Marks R. Nester

Extensions

a(0)=1 prepended and terms a(28) and beyond from Andrew Howroyd, Oct 26 2019

Status

approved