A056278 Number of primitive (aperiodic) word structures of length n which contain exactly two different symbols.

0, 1, 3, 6, 15, 27, 63, 120, 252, 495, 1023, 2010, 4095, 8127, 16365, 32640, 65535, 130788, 262143, 523770, 1048509, 2096127, 4194303, 8386440, 16777200, 33550335, 67108608, 134209530, 268435455, 536854005, 1073741823, 2147450880, 4294966269, 8589869055, 17179869105

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. This is identical to A000740 for n>1.

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

Apart from initial term, this is a duplicate of A000740.

Column 2 of A137651.

Cf. A056267.

Formula

a(n) = Sum_{d|n} mu(d)*A000225(n/d-1) where n>0.

G.f.: Sum_{k>=1} mu(k) * x^(2*k) / ((1 - x^k) * (1 - 2*x^k)). - Ilya Gutkovskiy, Apr 15 2021

Extensions

Terms a(30) and beyond from Andrew Howroyd, Apr 15 2021