A073997 Number of strings of length n over GF(4) with trace 1 and subtrace 0.

1, 2, 3, 16, 76, 272, 1008, 4096, 16576, 65792, 261888, 1048576, 4197376, 16781312, 67104768, 268435456, 1073790976, 4295032832, 17179803648, 68719476736, 274878693376, 1099512676352, 4398045462528, 17592186044416, 70368756760576, 281474993487872, 1125899890065408, 4503599627370496, 18014398710808576

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 16 2002

Keywords

• easy
• nonn

Comments

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.

Links

• F. Ruskey Strings over GF(4) with given trace and subtrace

Crossrefs

Cf. A073995, A073996, A073998, A073999, A074000.

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^3-3*q^2+4*q-1)*q/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004

Extensions

More terms from Max Alekseyev, Apr 16 2013