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

1,2

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

Table of n, a(n) for n=1..29.

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

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

Crossrefs

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

Sequence in context: A209004 A329121 A368765 * A007118 A012572 A371613

Adjacent sequences: A073994 A073995 A073996 * A073998 A073999 A074000

Keyword

easy,nonn

Author

Frank Ruskey and Nate Kube, Aug 16 2002

Extensions

More terms from Max Alekseyev, Apr 16 2013

Status

approved