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A073996
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Number of strings of length n over GF(4) with trace 0 and subtrace 1.
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4
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0, 0, 1, 3, 12, 60, 256, 1008, 4032, 16320, 65536, 261888, 1047552, 4193280, 16777216, 67104768, 268419072, 1073725440, 4294967296, 17179803648, 68719214592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Same as the number of strings of length n over GF(4) with trace 0 and subtrace x where x=RootOf(z^2+z+1). Same as the number of strings of length n over GF(4) with trace 0 and subtrace y 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.: (6*q^2-3*q+1)*q^2/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
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EXAMPLE
| a(2;0,1)=1 since the one 4-ary string of trace 0, subtrace 1 and length 2 is { 11 }.
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MATHEMATICA
| CoefficientList[Series[x^2 (6x^2-3x+1)/((1-2x)(1-4x)(1+4x^2)), {x, 0, 30}], x] (* From Harvey P. Dale, Apr 03 2011 *)
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CROSSREFS
| Cf. A073995, A073997, A073998, A073999, A074000.
Sequence in context: A090830 A127918 A069944 * A003483 A128602 A092803
Adjacent sequences: A073993 A073994 A073995 * A073997 A073998 A073999
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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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EXTENSIONS
| More terms from Harvey P. Dale, Apr 03 2011.
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