OFFSET
0,1
COMMENTS
Any diagonal, read top down from right to left, expresses a periodic sequence of 0's and 1's. Lengths of the periods are always powers of 2. Here below the periods for the first 20 diagonals:
01
0
1100
1100
1110
0
00011110
10010110
00101000
00011110
10000100
01001000
00011010
1110
0101011110101000
1011000101001110
0111111011010100
1000100101110110
0111011101000100
1011010110000110
LINKS
Paolo P. Lava, Picture of Triangle A141743
EXAMPLE
...............................0 First Row
............................1.... Add 1 to have an odd number of adjacent 1's
..............................0 First Row
............................1.0.. Add 0 because there is an odd number of adjacent 1's (second row)
..............................0 First Row
............................1.0.1 Again add 1 because there is a null number of adjacent 1's.
The second row is now complete.
..............................0 First Row
............................1.0.1 Second Row
..........................0... Add 0 because there is only an 1 adjacent (second row)
..............................1 First Row
............................1.0.1 Second Row
..........................0.0.... Add 0 because there is only an 1 adjacent (second row)
.............................0 First Row
...........................1.0.1 Second Row
.........................0.0.1 Add 1 because there are two 1's adjacent (second row)
.............................0 First Row
...........................1.0.1 Second Row
.........................0.0.1.1 Add 1 because there are two 1's adjacent (second and third row)
.............................0 First Row
...........................1.0.1 Second Row
.........................0.0.1.1.1 Add 1 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.
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Jul 07 2008
STATUS
approved