%I #21 Aug 21 2024 01:56:17

%S 1,1,1,1,1,2,4,8,15,27,48,85,155,288,541,1024,1935,3654,6912,13107,

%T 24940,47616,91136,174760,335626,645435,1242904,2396745,4627915,

%U 8947294,17317888,33554432,65076240,126324495,245428574,477218560,928638035,1808400384,3524068955

%N Number of binary Lyndon words of length n with trace 1 and subtrace 0 over Z_2.

%C Same as the number of binary Lyndon words of length n with trace 1 and subtrace 0 over GF(2).

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</a>

%H F. Ruskey, <a href="http://combos.org/TSlyndonZ2">Binary Lyndon words with given trace and subtrace</a>

%H F. Ruskey, <a href="http://combos.org/TSlyndonF2">Binary Lyndon words with given trace and subtrace over GF(2)</a>

%F a(2n) = A042982(2n), a(2n+1) = A049281(2n+1). This follows from Cattell et al. (see A042979), Main Theorem on p. 33 and Theorem 4 on p. 44.

%e a(3;1,0)=1 since the one binary Lyndon word of trace 1, subtrace 0 and length 3 is { 001 }.

%Y Cf. A074027, A074028, A074030.

%K easy,nonn

%O 1,6

%A _Frank Ruskey_ and Nate Kube, Aug 21 2002

%E Terms a(33) onward from _Max Alekseyev_, Apr 09 2013