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

0,3

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.

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

Crossrefs

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

Sequence in context: A091053 A095064 A323144 * A111274 A133385 A349148

Adjacent sequences: A056350 A056351 A056352 * A056354 A056355 A056356

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved