A056282 Number of primitive (aperiodic) word structures of length n which contain exactly six different symbols.

0, 0, 0, 0, 0, 1, 21, 266, 2646, 22827, 179487, 1323651, 9321312, 63436352, 420693273, 2734926292, 17505749898, 110687248392, 693081601779, 4306078872557, 26585679462783, 163305339165738, 998969857983405

Offset

1,7

Comments

Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same 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..23.

Formula

a(n) = Sum_{n > 0, d|n} mu(d)*A000770(n/d).

G.f.: Sum_{k>=1} mu(k) * x^(6*k) / Product_{j=1..6} (1 - j*x^k). - Ilya Gutkovskiy, Apr 15 2021

Crossrefs

Column 6 of A137651.

Cf. A056271.

Sequence in context: A169895 A092794 A133717 * A000770 A327507 A133105

Adjacent sequences: A056279 A056280 A056281 * A056283 A056284 A056285

Keyword

nonn

Author

Marks R. Nester

Status

approved