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A073997
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Number of strings of length n over GF(4) with trace 1 and subtrace 0.
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4
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1, 2, 3, 16, 76, 272, 1008, 4096, 16576, 65792, 261888, 1048576, 4197376, 16781312, 67104768
(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 0 where x=RootOf(z^2+z+1). Same as the number of strings of length n over GF(4) with trace y and subtrace 0 where y=1+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^3-3*q^2+4*q-1)*q/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
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CROSSREFS
| Cf. A073995, A073996, A073998, A073999, A074000.
Sequence in context: A052506 A052858 A191416 * A007118 A012572 A067848
Adjacent sequences: A073994 A073995 A073996 * A073998 A073999 A074000
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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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