|
|
A335617
|
|
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)).
|
|
0
|
|
|
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, 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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Conjectured quasiperiodicity with autocorrelation function R(x) = 1/2 if x = 0, 1/4 if x > 0.
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?
|
|
LINKS
|
|
|
MATHEMATICA
|
c[n_]:=c[n]=(c[n-1]-2c[n-2]+c[n-3])/n;
c[1] = 0; c[2] = 0; c[3] = 1;
Table[Ceiling@c[j], {j, 1, 2^7}]
|
|
CROSSREFS
|
Cf. A083035, A285305, A190843, A286059, A288213, A288551, A288473, A176405, A188321, A188398, A191162, A272170, A197879, A078588, A272532, A273129,A074937, A188297, A289128.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|