A056364 Number of primitive (period n) bracelet structures using a maximum of five different colored beads.

1, 1, 1, 2, 5, 11, 32, 88, 315, 1134, 4691, 19838, 88467, 399679, 1839857, 8533474, 39893579, 187393549, 884152226, 4185740194, 19876589828, 94633345517, 451615299593, 2159769331316, 10348546459872, 49672000435712, 238804870806677, 1149792978953236, 5543621480301561

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)*A056355(n/d) for n > 0.

a(n) = Sum_{k=1..5} A276543(n, k) for n > 0. - Andrew Howroyd, Oct 26 2019

Crossrefs

Cf. A056301, A056355, A056369, A276543.

Sequence in context: A124483 A079571 A151395 * A205799 A296549 A056365

Adjacent sequences: A056361 A056362 A056363 * A056365 A056366 A056367

Keyword

nonn

Author

Marks R. Nester

Extensions

a(0)=1 prepended and terms a(25) and beyond from Andrew Howroyd, Oct 26 2019

Status

approved