A053562 Number of ternary Lyndon words of length n with trace 1 and subtrace 0 over GF(3). Same as the number of ternary Lyndon words of length n with trace 2 and subtrace 0 over GF(3).

1, 1, 1, 2, 6, 13, 32, 87, 243, 654, 1782, 4914, 13664, 37994, 106288, 298890, 844182, 2391363, 6796160, 19369708, 55345784, 158489298, 454795398, 1307541690, 3765741324, 10862688116, 31381059609, 90780903460, 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, 0, 1); d|n, d=1(3) + (1/n) Sum mu(d) M(n/d, 0, 2); 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) = 3 = |{ 0001, 1222 }|

Crossrefs

Cf. A053548, A053560, A053561, A053563, A053564.

Sequence in context: A258344 A099232 A280758 * A003039 A109385 A244578

Adjacent sequences: A053559 A053560 A053561 * A053563 A053564 A053565

Keyword

nonn

Author

Frank Ruskey, Jan 17 2000

Status

approved