%I #28 Nov 10 2020 22:58:20
%S 0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,
%T 0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,
%U 1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1
%N Let c(1) = c(2) = 0, c(3) = 1, and c(n + 3) = (c(n) - 2*c(n + 1) + c(n + 2))/n, then a(n) = ceiling (c(n)).
%C Conjectured quasiperiodicity with autocorrelation function R(x) = 1/2 if x = 0, 1/4 if x > 0.
%C Some other proved or conjectured (or suspected) nonperiodic binary sequences where there are no more than two consecutive 0's or 1's include: A083035, A285305, A190843, A286059, A288213, A288551, A288473, A176405, A188321, A188398, A191162, A272170, A197879, A078588, A272532, A273129, A074937, A188297, A289128. Others?
%t c[n_]:=c[n]=(c[n-1]-2c[n-2]+c[n-3])/n;
%t c[1] = 0; c[2] = 0; c[3] = 1;
%t Table[Ceiling@c[j],{j,1,2^7}]
%Y Cf. A083035, A285305, A190843, A286059, A288213, A288551, A288473, A176405, A188321, A188398, A191162, A272170, A197879, A078588, A272532, A273129,A074937, A188297, A289128.
%K nonn
%O 0,1
%A _Andres Cicuttin_, Oct 11 2020