1,2

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.

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.: -(2*q^2+5*q-2)*q^2/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004

a(2; x,y)=2 since the two 4-ary strings of trace x, subtrace y and length 2 are { 1y, y1 }.

Cf. A073995, A073996, A073997, A073999, A074000.

Sequence in context: A000512 A084079 A042689 this_sequence A129444 A079815 A006883

Adjacent sequences: A073995 A073996 A073997 this_sequence A073999 A074000 A074001

easy,nonn

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