login
Number of primitive (aperiodic) word structures of length n which contain exactly three different symbols.
3

%I #15 Apr 15 2021 16:38:57

%S 0,0,1,6,25,89,301,960,3024,9305,28501,86430,261625,788669,2375075,

%T 7140720,21457825,64435896,193448101,580597110,1742343323,5228050949,

%U 15686335501,47063113320,141197991000,423610488665,1270865802276,3812663735790,11438127792025,34314649427035

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

%C Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same structure.

%D 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]

%H Andrew Howroyd, <a href="/A056279/b056279.txt">Table of n, a(n) for n = 1..500</a>

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

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

%Y Column 3 of A137651.

%Y Cf. A056268.

%K nonn

%O 1,4

%A _Marks R. Nester_

%E Terms a(26) and beyond from _Andrew Howroyd_, Apr 15 2021