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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
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OFFSET
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0,1
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COMMENTS
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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
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EXAMPLE
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.....................................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
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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STATUS
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approved
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