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A141728
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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.
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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
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LINKS
| Paolo P. Lava, Picture of Triangle A141728
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EXAMPLE
| .....................................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.
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CROSSREFS
| Cf. A141727, A141729-A141746.
Sequence in context: A168553 A068430 A141738 * A141737 A089011 A095111
Adjacent sequences: A141725 A141726 A141727 * A141729 A141730 A141731
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Jul 02 2008
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