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%I #15 May 03 2019 07:17:48
%S 1,2,3,16,76,272,1008,4096,16576,65792,261888,1048576,4197376,
%T 16781312,67104768,268435456,1073790976,4295032832,17179803648,
%U 68719476736,274878693376,1099512676352,4398045462528,17592186044416,70368756760576,281474993487872,1125899890065408,4503599627370496,18014398710808576
%N Number of strings of length n over GF(4) with trace 1 and subtrace 0.
%C 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.
%H F. Ruskey <a href="http://combos.org/TSstringF4">Strings over GF(4) with given trace and subtrace</a>
%F 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).
%F G.f.: -(2*q^3-3*q^2+4*q-1)*q/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
%Y Cf. A073995, A073996, A073998, A073999, A074000.
%K easy,nonn
%O 1,2
%A _Frank Ruskey_ and Nate Kube, Aug 16 2002
%E More terms from _Max Alekseyev_, Apr 16 2013