A074027 - OEIS

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A074027

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

1, 0, 0, 0, 1, 2, 5, 8, 15, 24, 45, 80, 155, 288, 550, 1024, 1935, 3626, 6885, 13056, 24940, 47616, 91225, 174760, 335626, 645120, 1242600, 2396160, 4627915, 8947294, 17318945, 33554432, 65076240, 126320640, 245424829, 477211280, 928638035, 1808400384, 3524082400

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OFFSET

1,6

COMMENTS

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

LINKS

Table of n, a(n) for n=1..39.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, Binary Lyndon words with given trace and subtrace

F. Ruskey, Binary Lyndon words with given trace and subtrace over GF(2)

FORMULA

a(2n) = A042979(2n), a(2n+1) = A042980(2n+1). This follows from Cattell et al. (see A042979), Main Theorem on p. 33 and Theorem 4 on p. 44.