A074028 Number of binary Lyndon words of length n with trace 0 and subtrace 1 over Z_2.

0, 0, 1, 1, 2, 2, 4, 6, 13, 24, 48, 85, 160, 288, 541, 1008, 1920, 3626, 6912, 13107, 24989, 47616, 91136, 174590, 335462, 645120, 1242904, 2396745, 4628480, 8947294, 17317888, 33552384, 65074253, 126320640, 245428574, 477218560, 928645120, 1808400384, 3524068955

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 1 over GF(2).

Examples

			a(5;0,1)=2 since the two binary Lyndon words of trace 0, subtrace 1 and length 5 are { 00011, 00101 }.
		

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. A074027, A074029, A074030.

Formula

a(2n) = A042980(2n), a(2n+1) = A042979(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