A056306 Number of primitive (period n) n-bead necklace structures using exactly five different colored beads.

0, 0, 0, 0, 1, 3, 20, 136, 773, 4280, 22430, 115097, 577577, 2863207, 14051163, 68515378, 332514803, 1608799915, 7767857090, 37460384315, 180536313527, 869901375049, 4192038616700, 20208367780744

Offset

1,6

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]

Links

Table of n, a(n) for n=1..24.

Formula

Sum mu(d)*A056298(n/d) where d|n. Alternatively, A056301(n)-A056300(n)..

Crossrefs

Column 5 of A107424.

Cf. A056290.

Sequence in context: A000276 A216778 A337105 * A056298 A114479 A074574

Adjacent sequences: A056303 A056304 A056305 * A056307 A056308 A056309

Keyword

nonn

Author

Marks R. Nester

Status

approved