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A073947
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Number of strings over Z_3 of length n with trace 0 and subtrace 0.
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5
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1, 1, 3, 9, 21, 63, 225, 729, 2187, 6561, 19845, 59535, 177633, 531441, 1594323, 4782969, 14344533, 43033599, 129127041, 387420489
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Same as number of strings over GF(3) of length n with trace 0 and subtrace 0.
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LINKS
| F. Ruskey, Strings over Z_3 of given Trace and Subtrace
F. Ruskey, Strings over GF(3) of given Trace and Subtrace
Index to sequences with linear recurrences with constant coefficients, signature (6,-15,27,-36,27).
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FORMULA
| 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.: q*(21*q^4-21*q^3+12*q^2-5*q+1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004
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EXAMPLE
| a(3;0,0)=3 since the three ternary strings of trace 0, subtrace 0 and length 3 are { 000, 111, 222 }.
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CROSSREFS
| Cf. A073948, A073949, A073950, A073951, A073952.
Sequence in context: A147078 A146416 A004667 * A062811 A001470 A118932
Adjacent sequences: A073944 A073945 A073946 * A073948 A073949 A073950
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KEYWORD
| easy,nonn
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AUTHOR
| Frank Ruskey, Nate Kube (ruskey(AT)cs.uvic.ca), Aug 15 2002
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