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A141727
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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 0 if the number of adjacent 1's is even or add 1 if it is odd. See example below.
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19
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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, 1, 0, 0, 1, 0
(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's and 1's Lengths of the periods are always powers of 2. Here below 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 great number of rows we get a nice representation with several big islands of zeros.
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LINKS
| Paolo P. Lava, Picture of Triangle A141727
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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 (first and second row)
......................................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.
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CROSSREFS
| Cf. A141728-A141746.
Sequence in context: A134842 A167753 A086747 * A123594 A145006 A080813
Adjacent sequences: A141724 A141725 A141726 * A141728 A141729 A141730
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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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