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Search: id:A053548
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| A053548 |
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Number of ternary Lyndon words of length n with trace 0 and subtrace 0 over GF(3). |
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+0
6
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| 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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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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.
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LINKS
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F. Ruskey, Ternary Lyndon words of given trace and subtrace over GF(3)
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FORMULA
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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!) )
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EXAMPLE
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a(4) = 2 = |{ 0111, 0222 }|
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CROSSREFS
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Cf. A053560, A053561, A053562, A053563, A053564.
Sequence in context: A007876 A005095 A092329 this_sequence A054119 A151891 A005204
Adjacent sequences: A053545 A053546 A053547 this_sequence A053549 A053550 A053551
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KEYWORD
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nonn
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AUTHOR
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Frank Ruskey (fruskey(AT)cs.uvic.ca), Jan 16 2000
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