A141728 Triangle read by rows T(n,k). Triangle elements are 0 and 1. Starting with 1 in the top add below a second row of (2n-1) elements (with n=2 -> 3). Moving from left to right add 1 if the number of adjacent 1's is even or add 0 if it is odd. See example below.

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

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

• easy
• nonn
• tabf

Comments

Any diagonal, read top down from right to left, expresses a periodic sequence of 0'0's and 1's Lengths of the periods are alway powers of 2. Here below the periods for the first 20 diagonals:

10

0

0110

0110

1000

0

01011010

00011110

11011000

11110000

11001010

01100000

01000110

0110

1011011101001000

0111111110000000

0000111101011010

1110000100011110

0100000111011000

1001011100001110

Examples

			.....................................1 First Row
..................................0 ... Add 0 to have an odd number of adjacent 1's
.....................................1 First Row
...................................0.0 ... Add again 0 to have an odd number of adjacent 1's
......................................1 First Row
...................................0.0.0 ... Again add 0 to have an odd number of adjacent 1's
The second row is now complete.
.....................................1 First Row
...................................0.0.0 Second Row
.................................1 ... Add 1 because there are no adjacent 1's
.....................................1 First Row
...................................0.0.0 Second Row
.................................1.0 ... Add 0 because there is one adjacent 1 (third row)
.....................................1 First Row
...................................0.0.0 Second Row
.................................1.0.1 ... Add 1 because there is no adjacent 1
.....................................1 First Row
...................................0.0.0 Second Row
.................................1.0.1.0 ... Add 0 because there is only an 1 adjacent (third row)
.....................................1 First Row
...................................0.0.0 Second Row
.................................1.0.1.0.1 ... Add 1 because there is no adjacent 1
The third row is now complete. Then repeat the process for the other rows.
		

Links

• Paolo P. Lava, Picture of Triangle A141728

Crossrefs

Cf. A141727, A141729-A141746.