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A221146
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Table read by antidiagonals: (m+n) - (m XOR n).
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3
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0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 8, 2, 4, 2, 0, 0, 0, 4, 4, 8, 8, 4, 4, 0, 0, 0, 2, 0, 6, 8, 10, 8, 6, 0, 2, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 2, 4, 2, 0, 10, 12, 10, 0, 2, 4, 2, 0
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OFFSET
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0,5
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COMMENTS
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This sequence is related to two fractals: the Sierpinski gasket fractal and Peano filigree.
For the Sierpinski fractal the procedure is the following:
- write the number stored in the position (i,j) as i+j + d, where d stands for difference.
The array of the differences is
0 0 0 0
0 2 0 2
0 0 4 4
0 2 4 6
If this matrix is represented by colors we obtain the Sierpinski gasket; coordinates (i,j) contain a pixel with the color i XOR j.
If we follow the odd and even numbers of the XOR table we obtain the Peano curve.
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LINKS
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EXAMPLE
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Table begins:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 ...
0 0 4 4 0 0 4 4 0 0 4 4 0 0 4 4 ...
0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 ...
0 0 0 0 8 8 8 8 0 0 0 0 8 8 8 8 ...
0 2 0 2 8 10 8 10 0 2 0 2 8 10 8 10 ...
0 0 4 4 8 8 12 12 0 0 4 4 8 8 12 12 ...
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 ...
0 0 0 0 0 0 0 0 16 16 16 16 16 16 16 16 ...
0 2 0 2 0 2 0 2 16 18 16 18 16 18 16 18 ...
0 0 4 4 0 0 4 4 16 16 20 20 16 16 20 20 ...
0 2 4 6 0 2 4 6 16 18 20 22 16 18 20 22 ...
0 0 0 0 8 8 8 8 16 16 16 16 24 24 24 24 ...
0 2 0 2 8 10 8 10 16 18 16 18 24 26 24 26 ...
0 0 4 4 8 8 12 12 16 16 20 20 24 24 28 28 ...
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ...
...
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MATHEMATICA
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Table[m-BitXor[n, m-n], {m, 0, 15}, {n, 0, m}] (* Paolo Xausa, Mar 14 2024 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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