A056305 Number of primitive (period n) n-bead necklace structures using exactly four different colored beads.

0, 0, 0, 1, 2, 13, 50, 220, 866, 3435, 13250, 51061, 194810, 742601, 2823764, 10738660, 40843370, 155493872, 592614050, 2261622287, 8643289484, 33080907357, 126797503250, 486710920300, 1870851589552

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

Comments

Turning over the necklace is not allowed. Colors may be permuted without changing the necklace 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]

Crossrefs

Column 4 of A107424.

Cf. A056289.

Formula

Sum mu(d)*A056297(n/d) where d|n. Alternatively, A056300(n)-A002075(n)..