A074029 Number of binary Lyndon words of length n with trace 1 and subtrace 0 over Z_2.

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

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 1 and subtrace 0 over GF(2).

Examples

			a(3;1,0)=1 since the one binary Lyndon word of trace 1, subtrace 0 and length 3 is { 001 }.
		

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, A074028, A074030.

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.

Extensions

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