A053564 Number of ternary Lyndon words of length n with trace 1 and subtrace 2 over GF(3). Same as the number of ternary Lyndon words of length n with trace 2 and subtrace 2 over GF(3).

0, 0, 1, 3, 6, 13, 36, 93, 243, 645, 1782, 4914, 13608, 37890, 106288, 299025, 844182, 2391363, 6797196, 19371684, 55345784, 158486625, 454795398, 1307541690, 3765720066, 10862647236, 31381059609, 90780960426, 262951692390

Offset

1,4

Links

Table of n, a(n) for n=1..29.

F. Ruskey, Ternary Lyndon words with given trace and subtrace over GF(3)

Formula

(1/n) Sum mu(d) M(n/d, 1, 2); d|n, d=1, 2(3) where M(n, t, s) = Sum n!/(i!j!k!); i+j+k=n, j=t(3), k=s(3).

Example

a(4) = 3 = |{ 0112, 0121, 0211 }|

Crossrefs

Cf. A053548, A053560, A053561, A053562, A053563.

Sequence in context: A352864 A062466 A366940 * A264236 A216999 A036781

Adjacent sequences: A053561 A053562 A053563 * A053565 A053566 A053567

Keyword

nonn

Author

Frank Ruskey, Jan 17 2000

Status

approved