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A053548
Number of ternary Lyndon words of length n with trace 0 and subtrace 0 over GF(3).
6
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
1,4
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.
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]
EXAMPLE
a(4) = 2 = |{ 0111, 0222 }|
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank Ruskey, Jan 16 2000
STATUS
approved