A056280 Number of primitive (aperiodic) word structures of length n which contain exactly four different symbols.

0, 0, 0, 1, 10, 65, 350, 1700, 7770, 34095, 145750, 611435, 2532530, 10391395, 42355940, 171797200, 694337290, 2798799150, 11259666950, 45232081795, 181509069700, 727778478075, 2916342574750, 11681056021300, 46771289738800, 187226354413735, 749329038527580

Offset

1,5

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

Andrew Howroyd, Table of n, a(n) for n = 1..500

Formula

a(n) = Sum_{n > 0, d|n} mu(d)*A000453(n/d).

G.f.: Sum_{k>=1} mu(k) * x^(4*k) / Product_{j=1..4} (1 - j*x^k). - Ilya Gutkovskiy, Apr 15 2021

Crossrefs

Column 4 of A137651.

Cf. A056269.

Sequence in context: A346976 A354397 A003519 * A000453 A365532 A365525

Adjacent sequences: A056277 A056278 A056279 * A056281 A056282 A056283

Keyword

nonn

Author

Marks R. Nester

Extensions

Terms a(25) and beyond from Andrew Howroyd, Apr 15 2021

Status

approved