

A053548


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


5



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
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OFFSET

1,4


COMMENTS

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


LINKS

Table of n, a(n) for n=1..29.
F. Ruskey, Ternary Lyndon words of given trace and subtrace over GF(3)


FORMULA

Sum{ d divides n, d==1, 2(3) }mu(d)(M(n/d, 0, 0)[3d divides n]3^{n/(3d)}), where M(n, t, s) = Sum{ i+j+k=n, j=t(3), k=s(3) }( n!/(i!j!k!) )


EXAMPLE

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


CROSSREFS

Cf. A053560, A053561, A053562, A053563, A053564.
Sequence in context: A243789 A214935 A092329 * A054119 A259490 A274758
Adjacent sequences: A053545 A053546 A053547 * A053549 A053550 A053551


KEYWORD

nonn


AUTHOR

Frank Ruskey, Jan 16 2000


STATUS

approved



