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

Author

Marks R. Nester

Keywords

• nonn

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

Crossrefs

Cf. A056302, A056356, A056370, A276543.

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

Extensions

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