1,3

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.

F. Ruskey Number of strings over GF(4) of given trace and subtrace

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

a(2;0,1)=1 since the one 4-ary string of trace 0, subtrace 1 and length 2 is { 11 }.

Cf. A073995, A073997, A073998, A073999, A074000.

Sequence in context: A090830 A127918 A069944 this_sequence A003483 A128602 A092803

Adjacent sequences: A073993 A073994 A073995 this_sequence A073997 A073998 A073999

easy,nonn

Frank Ruskey, Nate Kube (fruskey(AT)cs.uvic.ca), Aug 16 2002