%I #9 May 03 2019 07:49:05
%S 1,1,1,2,6,13,32,87,243,654,1782,4914,13664,37994,106288,298890,
%T 844182,2391363,6796160,19369708,55345784,158489298,454795398,
%U 1307541690,3765741324,10862688116,31381059609,90780903460,262951692390
%N Number of ternary Lyndon words of length n with trace 1 and subtrace 0 over GF(3). Same as the number of ternary Lyndon words of length n with trace 2 and subtrace 0 over GF(3).
%H F. Ruskey, <a href="http://combos.org/TSlyndonF3">Ternary Lyndon words with given trace and subtrace over GF(3)</a>
%F (1/n) Sum mu(d) M(n/d, 0, 1); d|n, d=1(3) + (1/n) Sum mu(d) M(n/d, 0, 2); d|n, d=2(3) where M(n, t, s) = Sum n!/(i!j!k!); i+j+k=n, j=t(3), k=s(3).
%e a(4) = 3 = |{ 0001, 1222 }|
%Y Cf. A053548, A053560, A053561, A053563, A053564.
%K nonn
%O 1,4
%A _Frank Ruskey_, Jan 17 2000