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

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.

Example

a(6;0,0)=2 since the two binary Lyndon words of trace 0, subtrace 0 and length 6 are { 001111, 010111 }.

Crossrefs

Cf. A074028, A074029, A074030.

Sequence in context: A078697 A066629 A154327 * A018156 A051293 A081660

Adjacent sequences: A074024 A074025 A074026 * A074028 A074029 A074030

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