A141743 Triangle read by rows T(n,k). Triangle elements are 0 and 1. Starting with 0 in the top add below a second row of (2n-1) elements (with n=2 -> 3). Moving from left to right add 0 if the number of adjacent 1's is odd or add 1 if it is even or null. See example below.

0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 07 2008

Keywords

• easy
• nonn
• tabf

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

Examples

			...............................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.
		

Links

• Paolo P. Lava, Picture of Triangle A141743