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

Author

Frank Ruskey and Nate Kube, Aug 21 2002

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

• 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)

Crossrefs

Cf. A074028, A074029, A074030.

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.

Extensions

Terms a(33) onward from Max Alekseyev, Apr 09 2013