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

1,4

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_{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

Crossrefs

Column 3 of A137651.

Cf. A056268.

Sequence in context: A099625 A209243 A143628 * A055337 A309946 A001871

Adjacent sequences: A056276 A056277 A056278 * A056280 A056281 A056282

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved