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Search: id:A141743
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| A141743 |
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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. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Any diagonal, read top down from right to left, expresses a periodic sequence of 0's and 1's Lengths of the periods are alway 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
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EXAMPLE
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...............................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 thereis 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.
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CROSSREFS
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Adjacent sequences: A141740 A141741 A141742 this_sequence A141744 A141745 A141746
Sequence in context: A135993 A092202 A082848 this_sequence A112416 A061265 A125122
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jul 07 2008
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