cp's OEIS Frontend

A073999 Number of strings of length n over GF(4) with trace 1 and subtrace x where x = RootOf(z^2+z+1).

%I A073999 #27 Jul 20 2021 17:11:02
%S A073999 0,0,3,16,60,240,1008,4096,16320,65280,261888,1048576,4193280,
%T A073999 16773120,67104768,268435456,1073725440,4294901760,17179803648,
%U A073999 68719476736,274877644800,1099510579200,4398045462528,17592186044416,70368739983360,281474959933440,1125899890065408,4503599627370496,18014398442373120
%N A073999 Number of strings of length n over GF(4) with trace 1 and subtrace x where x = RootOf(z^2+z+1).
%C A073999 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.
%H A073999 F. Ruskey, <a href="http://combos.org/TSstringF4">Strings over GF(4) with given trace and subtrace</a>
%H A073999 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,24,-32).
%F A073999 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).
%F A073999 G.f.: -(2*q-3)*q^3/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004
%F A073999 a(n) = -2^(n-3) +( (-2i)^n + (2i)^n +4^n )/16 with i=sqrt(-1). - _R. J. Mathar_, Nov 18 2011
%t A073999 LinearRecurrence[{6,-12,24,-32},{0,0,3,16},30] (* _Harvey P. Dale_, Mar 12 2019 *)
%Y A073999 Cf. A073995, A073996, A073997, A073998.
%K A073999 easy,nonn
%O A073999 1,3
%A A073999 _Frank Ruskey_ and Nate Kube, Aug 16 2002
%E A073999 More terms from _Max Alekseyev_, Apr 16 2013