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A073998
Number of strings of length n over GF(4) with trace 1 and subtrace 1.
9
0, 2, 7, 16, 60, 272, 1072, 4096, 16320, 65792, 262912, 1048576, 4193280, 16781312, 67121152, 268435456, 1073725440, 4295032832, 17180065792, 68719476736, 274877644800, 1099512676352, 4398049656832, 17592186044416, 70368739983360, 281474993487872, 1125899957174272, 4503599627370496, 18014398442373120
OFFSET
1,2
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.
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
EXAMPLE
a(2; x,y)=2 since the two 4-ary strings of trace x, subtrace y and length 2 are { 1y, y1 }.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Frank Ruskey and Nate Kube, Aug 16 2002
EXTENSIONS
More terms from Max Alekseyev, Apr 16 2013
STATUS
approved