A056365 Number of primitive (period n) bracelet structures using a maximum of six different colored beads.

1, 1, 1, 2, 5, 11, 33, 91, 342, 1305, 5940, 28227, 144545, 760109, 4112455, 22571026, 125410006, 702370207, 3959138462, 22425417823, 127530807883, 727630240442, 4163114784625, 23876534534361, 137228556011456, 790200525479694, 4557943660168122, 26331300028827092

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)*A056356(n/d) for n > 0.

a(n) = Sum_{k=1..6} A276543(n, k) for n > 0. - Andrew Howroyd, Oct 26 2019

Crossrefs

Cf. A056302, A056356, A056370, A276543.

Sequence in context: A056364 A205799 A296549 * A276548 A353016 A006400

Adjacent sequences: A056362 A056363 A056364 * A056366 A056367 A056368

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