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%I #14 Mar 26 2022 12:45:35
%S 0,0,6,36,150,534,1806,5760,18144,55830,171006,518580,1569750,4732014,
%T 14250450,42844320,128746950,386615376,1160688606,3483582660,
%U 10454059938,31368305694,94118013006,282378679920,847187946000,2541662931990,7625194813656,22875982414740
%N Number of primitive (aperiodic) words of length n which contain exactly three different symbols.
%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]
%F a(n) = Sum_{d|n} mu(d)*A001117(n/d).
%o (PARI) f(n) = 3^n - 3*2^n + 3;
%o a(n) = sumdiv(n, d, moebius(d)*f(n/d)); \\ _Michel Marcus_, Mar 25 2022
%Y Cf. A000244, A001117, A008683, A054718.
%K nonn
%O 1,3
%A _Marks R. Nester_
%E a(11) and following corrected by _Georg Fischer_, Mar 24 2022
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