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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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10
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0, 0, 3, 16, 60, 240, 1008, 4096, 16320, 65280, 261888, 1048576, 4193280, 16773120, 67104768, 268435456, 1073725440, 4294901760, 17179803648, 68719476736, 274877644800, 1099510579200, 4398045462528, 17592186044416, 70368739983360, 281474959933440, 1125899890065408, 4503599627370496, 18014398442373120
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OFFSET
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1,3
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COMMENTS
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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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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
a(n) = -2^(n-3) +( (-2i)^n + (2i)^n +4^n )/16 with i=sqrt(-1). - R. J. Mathar, Nov 18 2011
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MATHEMATICA
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LinearRecurrence[{6, -12, 24, -32}, {0, 0, 3, 16}, 30] (* Harvey P. Dale, Mar 12 2019 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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