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A073998
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Number of strings of length n over GF(4) with trace 1 and subtrace 1.
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4
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0, 2, 7, 16, 60, 272, 1072, 4096, 16320, 65792, 262912, 1048576, 4193280, 16781312, 67121152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Same as the number of strings of length n over GF(4) with trace x and subtrace y where x=RootOf(z^2+z+1) and y=1+x. Same as the number of strings of length n over GF(4) with trace y and subtrace x.
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LINKS
| F. Ruskey Number of strings over GF(4) of given trace and subtrace
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FORMULA
| a(n; t, s) = a(n-1; t, s) + a(n-1; t-1, s-(t-1)) + a(n-1; t-2, s-2(t-2)) + a(n-1; t-3, s-3(t-3)) where t is the trace and s is the subtrace. Note that all operations involving operands t or s are carried out over GF(4).
G.f.: -(2*q^2+5*q-2)*q^2/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
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EXAMPLE
| a(2; x,y)=2 since the two 4-ary strings of trace x, subtrace y and length 2 are { 1y, y1 }.
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CROSSREFS
| Cf. A073995, A073996, A073997, A073999, A074000.
Sequence in context: A000512 A084079 A042689 * A129444 A079815 A006883
Adjacent sequences: A073995 A073996 A073997 * A073999 A074000 A074001
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KEYWORD
| easy,nonn
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AUTHOR
| Frank Ruskey, Nate Kube (ruskey(AT)cs.uvic.ca), Aug 16 2002
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