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A074029
Number of binary Lyndon words of length n with trace 1 and subtrace 0 over Z_2.
7
1, 1, 1, 1, 1, 2, 4, 8, 15, 27, 48, 85, 155, 288, 541, 1024, 1935, 3654, 6912, 13107, 24940, 47616, 91136, 174760, 335626, 645435, 1242904, 2396745, 4627915, 8947294, 17317888, 33554432, 65076240, 126324495, 245428574, 477218560, 928638035, 1808400384, 3524068955
OFFSET
1,6
COMMENTS
Same as the number of binary Lyndon words of length n with trace 1 and subtrace 0 over GF(2).
FORMULA
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.
EXAMPLE
a(3;1,0)=1 since the one binary Lyndon word of trace 1, subtrace 0 and length 3 is { 001 }.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Frank Ruskey and Nate Kube, Aug 21 2002
EXTENSIONS
Terms a(33) onward from Max Alekseyev, Apr 09 2013
STATUS
approved