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Search: id:A073952
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| A073952 |
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Number of strings over Z_3 of length n with trace 1 and subtrace 2. |
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+0
6
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| 0, 0, 3, 12, 30, 81, 252, 756, 2187, 6480, 19602, 59049, 176904, 530712, 1594323, 4785156, 14351094, 43046721, 129146724, 387440172
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Same as number of strings over Z_3 of length n with trace 2 and subtrace 2. Same as number of strings over GF(3) of length n with trace 1 and subtrace 2. Same as number of strings over GF(3) of length n with trace 2 and subtrace 2.
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LINKS
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F. Ruskey, Strings over Z_3 of given Trace and Subtrace
F. Ruskey, Strings over GF(3) of given Trace and Subtrace
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FORMULA
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a(n; t, s) = a(n-1; t, s) + a(n-1; t+2, s+2t+1) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.
G.f.: 3q^3(q^2-2*q+1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004
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EXAMPLE
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a(3;1,2)=3 since the three ternay strings of trace 1, subtrace 2 and length 3 are { 112, 121, 211 }.
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CROSSREFS
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Cf. A073947, A073948, A073949, A073950, A073951.
Sequence in context: A048088 A064181 A089143 this_sequence A107231 A131936 A009135
Adjacent sequences: A073949 A073950 A073951 this_sequence A073953 A073954 A073955
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Ruskey, Nate Kube (fruskey(AT)cs.uvic.ca), Aug 15 2002
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