A056355 Number of bracelet structures using a maximum of five different colored beads.

1, 1, 2, 3, 7, 12, 36, 89, 322, 1137, 4704, 19839, 88508, 399680, 1839947, 8533488, 39893901, 187393550, 884153396, 4185740195, 19876594537, 94633345608, 451615319433, 2159769331317, 10348546548695, 49672000435724, 238804871206358, 1149792978954373, 5543621482141513

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

Formula

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

a(n) = Sum_{k=1..5} A152176(n, k) for n > 0. - Andrew Howroyd, Oct 25 2019

Crossrefs

Cf. A056293, A152176.

Sequence in context: A080107 A056156 A112837 * A056356 A084708 A035003

Adjacent sequences: A056352 A056353 A056354 * A056356 A056357 A056358

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved