A053561 Number of ternary Lyndon words of length n with trace 0 and subtrace 2 over GF(3).

0, 1, 2, 3, 6, 15, 36, 87, 234, 645, 1782, 4893, 13608, 37994, 106434, 299025, 844182, 2391723, 6797196, 19369708, 55342972, 158486625, 454795398, 1307534319, 3765720066, 10862688116, 31381118658, 90780960426, 262951692390

Offset

1,3

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, 1); d divides n, d=1(3) + (1/n) Sum mu(d) M(n/d, 2, 2); d divides n, d=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 = |{ 0012, 0021, 0102 }|

Crossrefs

Cf. A053548, A053560, A053562, A053563, A053564.

Sequence in context: A352901 A052102 A369628 * A237585 A147773 A006403

Adjacent sequences: A053558 A053559 A053560 * A053562 A053563 A053564

Keyword

nonn

Author

Frank Ruskey, Jan 17 2000

Status

approved