A056281 Number of primitive (aperiodic) word structures of length n which contain exactly five different symbols.

0, 0, 0, 0, 1, 15, 140, 1050, 6951, 42524, 246730, 1379385, 7508501, 40074895, 210766919, 1096189500, 5652751651, 28958088579, 147589284710, 749206047975, 3791262568261, 19137821665325, 96416888184100

Offset

1,6

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)*A000481(n/d).

G.f.: Sum_{k>=1} mu(k) * x^(5*k) / Product_{j=1..5} (1 - j*x^k). - Ilya Gutkovskiy, Apr 15 2021

Crossrefs

Column 5 of A137651.

Cf. A056270.

Sequence in context: A354394 A346977 A354398 * A000481 A365528 A327506

Adjacent sequences: A056278 A056279 A056280 * A056282 A056283 A056284

Keyword

nonn

Author

Marks R. Nester

Status

approved