A056353 Number of bracelet structures using a maximum of three different colored beads.

1, 1, 2, 3, 6, 9, 22, 40, 100, 225, 582, 1464, 3960, 10585, 29252, 80819, 226530, 636321, 1800562, 5107480, 14548946, 41538916, 118929384, 341187048, 980842804, 2824561089, 8147557742, 23536592235, 68087343148, 197216119545, 571924754778, 1660419530056, 4825588205920

Offset: 0

Author

Marks R. Nester

Keywords

• nonn

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
• R. M. Thompson and R. T. Downs, Systematic generation of all nonequivalent closest packed stacking sequences of length N using group theory, Acta Cryst. B57 (2001), 766-771; B58 (2002), 153.

Crossrefs

Cf. A002076, A000011, A027671, A114438, A152176.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.

a(n) = Sum_{k=1..3} A152176(n, k) for n > 0. - Andrew Howroyd, Oct 25 2019

Extensions

a(0)=1 prepended and terms a(28) and beyond from Andrew Howroyd, Oct 25 2019