

A073999


Number of strings of length n over GF(4) with trace 1 and subtrace x where x = RootOf(z^2+z+1).


6



0, 0, 3, 16, 60, 240, 1008, 4096, 16320, 65280, 261888, 1048576, 4193280, 16773120, 67104768, 268435456, 1073725440, 4294901760, 17179803648, 68719476736, 274877644800, 1099510579200, 4398045462528, 17592186044416, 70368739983360, 281474959933440, 1125899890065408, 4503599627370496, 18014398442373120
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Same as the number of strings of length n over GF(4) with trace x and subtrace 1. Same as the number of strings of length n over GF(4) with trace y and subtrace 1 where y = 1+x. Same as the number of strings of length n over GF(4) with trace 1 and subtrace y. Same as the number of strings of length n over GF(4) with trace x and subtrace x. Same as the number of strings of length n over GF(4) with trace y and subtrace y.


LINKS

Table of n, a(n) for n=1..29.
F. Ruskey, Strings over GF(4) with given trace and subtrace
Index entries for linear recurrences with constant coefficients, signature (6,12,24,32).


FORMULA

a(n; t, s) = a(n1; t, s) + a(n1; t1, s(t1)) + a(n1; t2, s2(t2)) + a(n1; t3, s3(t3)) 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*q3)*q^3/[(12q)(14q)(1+4q^2)].  Lawrence Sze, Oct 24 2004
a(n) = 2^(n3) +( (2i)^n + (2i)^n +4^n )/16 with i=sqrt(1).  R. J. Mathar, Nov 18 2011


MATHEMATICA

LinearRecurrence[{6, 12, 24, 32}, {0, 0, 3, 16}, 30] (* Harvey P. Dale, Mar 12 2019 *)


CROSSREFS

Cf. A073995, A073996, A073997, A073998.
Sequence in context: A005550 A210323 A062474 * A259056 A155160 A323941
Adjacent sequences: A073996 A073997 A073998 * A074000 A074001 A074002


KEYWORD

easy,nonn


AUTHOR

Frank Ruskey and Nate Kube, Aug 16 2002


EXTENSIONS

More terms from Max Alekseyev, Apr 16 2013


STATUS

approved



