A074030 Number of binary Lyndon words of length n with trace 1 and subtrace 1 over Z_2.

0, 0, 0, 1, 2, 3, 5, 8, 13, 24, 45, 85, 160, 297, 550, 1024, 1920, 3626, 6885, 13107, 24989, 47709, 91225, 174760, 335462, 645120, 1242600, 2396745, 4628480, 8948385, 17318945, 33554432, 65074253, 126320640, 245424829, 477218560, 928645120, 1808414181, 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 1 and subtrace 1 over GF(2).

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, A074029.

Formula

a(2n) = A042981(2n), a(2n+1) = A042982(2n+1). This follows from Cattell et al. (see A042979), Main Theorem on p. 33 and Theorem 4 on p. 44.

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006

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