A056279 Number of primitive (aperiodic) word structures of length n which contain exactly three different symbols.

0, 0, 1, 6, 25, 89, 301, 960, 3024, 9305, 28501, 86430, 261625, 788669, 2375075, 7140720, 21457825, 64435896, 193448101, 580597110, 1742343323, 5228050949, 15686335501, 47063113320, 141197991000, 423610488665, 1270865802276, 3812663735790, 11438127792025, 34314649427035

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

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

Crossrefs

Column 3 of A137651.

Cf. A056268.

Formula

a(n) = Sum_{d|n} mu(d)*A000392(n/d) where n>0.

G.f.: Sum_{k>=1} mu(k) * x^(3*k) / Product_{j=1..3} (1 - j*x^k). - Ilya Gutkovskiy, Apr 15 2021

Extensions

Terms a(26) and beyond from Andrew Howroyd, Apr 15 2021