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%I #20 Apr 15 2021 16:59:25
%S 0,0,0,1,10,65,350,1700,7770,34095,145750,611435,2532530,10391395,
%T 42355940,171797200,694337290,2798799150,11259666950,45232081795,
%U 181509069700,727778478075,2916342574750,11681056021300,46771289738800,187226354413735,749329038527580
%N Number of primitive (aperiodic) word structures of length n which contain exactly four 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="/A056280/b056280.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = Sum_{n > 0, d|n} mu(d)*A000453(n/d).
%F G.f.: Sum_{k>=1} mu(k) * x^(4*k) / Product_{j=1..4} (1 - j*x^k). - _Ilya Gutkovskiy_, Apr 15 2021
%Y Column 4 of A137651.
%Y Cf. A056269.
%K nonn
%O 1,5
%A _Marks R. Nester_
%E Terms a(25) and beyond from _Andrew Howroyd_, Apr 15 2021
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