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Search: id:A073999
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| A073999 |
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Number of strings of length n over GF(4) with trace 1 and subtrace x where x = RootOf(z^2+z+1). |
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+0
7
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| 0, 0, 3, 16, 60, 240, 1008, 4096, 16320, 65280, 261888, 1048576, 4193280, 16773120, 67104768
(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 the number of strings of length n over GF(4) with trace x and subtrace 1. Same as the number of strings of length n over GF(4) with trace y and subtrace 1 where y = 1+x. Same as the number of strings of length n over GF(4) with trace 1 and subtrace y. Same as the number of strings of length n over GF(4) with trace x and subtrace x. Same as the number of strings of length n over GF(4) with trace y and subtrace y.
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LINKS
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F. Ruskey Number of strings over GF(4) 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-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)*q^3/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
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CROSSREFS
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Cf. A073995, A073996, A073997, A073998.
Sequence in context: A099851 A005550 A062474 this_sequence A155160 A037451 A007143
Adjacent sequences: A073996 A073997 A073998 this_sequence A074000 A074001 A074002
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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 16 2002
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