OFFSET
0,1
COMMENTS
Any diagonal, read top down from right to left, is a periodic sequence of 0's and 1's. The lengths of the periods are always powers of 2. Here are the periods for the first 20 diagonals:
1
0
10
10
0110
0
0100
1000
11110000
1110
01001110
00101000
01011100
1000
11100000
11001110
0111000110001110
01101000
0011011010011100
0010001010001000
If we draw a large number of rows we obtain an interesting figure with several large islands of zeros.
LINKS
Paolo P. Lava, Picture of Triangle A141727
EXAMPLE
.....................................1 First Row
...................................1 ... Add 1 to have an even number of adjacent 1's (2)
.....................................1 First Row
...................................1.0 ... Add 0 because there are two adjacent 1's (in the first and second rows)
......................................1 First Row
....................................1.0.1 ... Again add 1 to have an even number of adjacent 1's (2)
The second row is now complete.
.....................................1 First Row
...................................1.0.1 Second Row
.................................1 ... Add 1 because there is only an 1 adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0 ... Add 0 because there are two 1's adjacent (second and third row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0 ... Again add 0 because there are two 1's adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0.1 ... Add 1 because there is only an 1 adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0.1.0 ... Add 0 because there are two 1's adjacent (second and third row)
The third row is now complete. Then repeat the process for the other rows.
The triangle begins:
...........................1
........................1..0..1
.....................1..0..0..1..0
..................1..0..1..0..1..0..0
...............1..0..0..1..1..0..1..1..1
............1..0..1..0..0..0..0..0..1..1..0
.........1..0..0..1..0..0..0..0..1..1..1..0..0
......1..0..1..0..1..0..0..0..1..1..0..0..1..1..1
...1..0..0..1..1..0..1..1..0..0..0..1..0..0..1..1..0
1..0..1..0..0..0..0..0..0..1..1..0..1..0..1..1..1..0..0
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Paolo P. Lava & Giorgio Balzarotti, Jul 02 2008
EXTENSIONS
Minor edits by N. J. A. Sloane, Sep 10 2012
STATUS
approved