%I #9 May 03 2019 07:49:02
%S 0,0,1,1,4,13,36,90,243,661,1804,4914,13608,37944,106288,298755,
%T 843796,2391363,6797196,19370696,55345784,158491993,454803100,
%U 1307541690,3765720066,10862667648,31381059609,90780846494,262951527460
%N Number of ternary Lyndon words of length n with trace 1 and subtrace 1 over GF(3). Same as the number of ternary Lyndon words of length n with trace 2 and subtrace 1 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, 2); d|n, d=1(3) + (1/n) Sum mu(d) M(n/d, 0, 1); 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) = 1 = |{ 0022 }|
%Y Cf. A053548, A053560, A053561, A053562, A053564.
%K nonn
%O 1,5
%A _Frank Ruskey_, Jan 17 2000