%I #12 Dec 27 2021 23:52:36
%S 1,0,0,2,4,9,32,90,240,654,1804,4950,13664,37944,106272,298890,843796,
%T 2390595,6796160,19370696,55345680,158489298,454803100,1307556162,
%U 3765741324,10862667648,31381058880,90780903460,262951527460
%N Number of ternary Lyndon words of length n with trace 0 and subtrace 0 over GF(3).
%C Trace is sum of digits, subtrace is sum of products of pairs of digits. [3|n] above is "Iversonian convention", 1 if 3|n, 0 otherwise.
%H F. Ruskey, <a href="http://combos.org/TSlyndonF3">Ternary Lyndon words with given trace and subtrace over GF(3)</a>
%F a(n) = (1/n) * Sum_{d divides n, d==1, 2(3)} mu(d) * (M(n/d, 0, 0)-[3*d divides n] * 3^{n/(3*d)}), where M(n, t, s) = Sum_{i+j+k=n, j=t(3), k=s(3)} n!/(i!*j!*k!). [Corrected by _Sean A. Irvine_, Dec 27 2021]
%e a(4) = 2 = |{ 0111, 0222 }|
%Y Cf. A053560, A053561, A053562, A053563, A053564.
%K nonn
%O 1,4
%A _Frank Ruskey_, Jan 16 2000