A053563 Number of ternary Lyndon words of length n with trace 1 and subtrace 1 over GF(3). Same as the number of ternary Lyndon words of length n with trace 2 and subtrace 1 over GF(3).

0, 0, 1, 1, 4, 13, 36, 90, 243, 661, 1804, 4914, 13608, 37944, 106288, 298755, 843796, 2391363, 6797196, 19370696, 55345784, 158491993, 454803100, 1307541690, 3765720066, 10862667648, 31381059609, 90780846494, 262951527460

Offset

1,5

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, 0, 2); d|n, d=1(3) + (1/n) Sum mu(d) M(n/d, 0, 1); d|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) = 1 = |{ 0022 }|

Crossrefs

Cf. A053548, A053560, A053561, A053562, A053564.

Sequence in context: A036629 A350642 A079922 * A221882 A235996 A036636

Adjacent sequences: A053560 A053561 A053562 * A053564 A053565 A053566

Keyword

nonn

Author

Frank Ruskey, Jan 17 2000

Status

approved