A056363 Number of primitive (period n) bracelet structures using a maximum of four different colored beads.

1, 1, 1, 2, 5, 10, 29, 72, 230, 700, 2421, 8308, 30070, 108990, 403188, 1497057, 5607200, 21076570, 79595257, 301492044, 1145558141, 4363503609, 16660196142, 63741248200, 244339616370, 938255682540, 3608668279965, 13900021843855, 53614339995060, 207062143625710

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)*A056354(n/d) for n > 0.

a(n) = Sum_{k=1..4} A276543(n, k) for n > 0. - Andrew Howroyd, Oct 26 2019

Crossrefs

Cf. A056300, A056354, A056368, A276543.

Sequence in context: A102964 A075885 A018377 * A006404 A101957 A047113

Adjacent sequences: A056360 A056361 A056362 * A056364 A056365 A056366

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved