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A074029 Number of binary Lyndon words of length n with trace 1 and subtrace 0 over Z_2. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Same as the number of binary Lyndon words of length n with trace 1 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) = 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.

EXAMPLE

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

CROSSREFS

Cf. A074027, A074028, A074030.

Sequence in context: A143281 A098057 A289692 * A248729 A138653 A284275

Adjacent sequences:  A074026 A074027 A074028 * A074030 A074031 A074032

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

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)