A053548 Number of ternary Lyndon words of length n with trace 0 and subtrace 0 over GF(3).

1, 0, 0, 2, 4, 9, 32, 90, 240, 654, 1804, 4950, 13664, 37944, 106272, 298890, 843796, 2390595, 6796160, 19370696, 55345680, 158489298, 454803100, 1307556162, 3765741324, 10862667648, 31381058880, 90780903460, 262951527460

Offset: 1

Author

Frank Ruskey, Jan 16 2000

Keywords

• nonn

Comments

Trace is sum of digits, subtrace is sum of products of pairs of digits. [3|n] above is "Iversonian convention", 1 if 3|n, 0 otherwise.

Examples

			a(4) = 2 = |{ 0111, 0222 }|
		

Links

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

Crossrefs

Cf. A053560, A053561, A053562, A053563, A053564.

Formula

a(n) = (1/n) * Sum_{d divides n, d==1, 2(3)} mu(d) * (M(n/d, 0, 0)-[3*d divides n] * 3^{n/(3*d)}), where M(n, t, s) = Sum_{i+j+k=n, j=t(3), k=s(3)} n!/(i!*j!*k!). [Corrected by Sean A. Irvine, Dec 27 2021]