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A210635
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Array read by descending antidiagonals: a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w), n >= 0, w >= 1.
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0
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0, 1, 1, 2, 0, 2, 3, 1, 3, 3, 4, 2, 0, 2, 4, 5, 3, 1, 5, 5, 5, 6, 4, 2, 0, 4, 4, 6, 7, 5, 3, 1, 7, 3, 7, 7, 8, 6, 4, 2, 0, 6, 8, 6, 8, 9, 7, 5, 3, 1, 9, 5, 7, 9, 9, 10, 8, 6, 4, 2, 0, 8, 4, 6, 8, 10, 11, 9, 7, 5, 3, 1, 11, 7, 11, 11, 11, 11, 12, 10, 8, 6, 4, 2, 0, 10, 6, 10, 10, 10, 12
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OFFSET
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0,4
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COMMENTS
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Each column is a permutation of the nonnegative integers.
Column w can be used to mirror horizontally an infinite rectangular image of width w stored in a array of pixels. The pixels in the first row of the image are numbered from 0 to w-1 and subsequent rows continue the numbering likewise.
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LINKS
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FORMULA
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a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w).
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EXAMPLE
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The transposed array begins:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17 16 19 18 ...
2 1 0 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 ...
3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 19 18 17 16 ...
4 3 2 1 0 9 8 7 6 5 14 13 12 11 10 19 18 17 16 15 ...
5 4 3 2 1 0 11 10 9 8 7 6 17 16 15 14 13 12 23 22 ...
6 5 4 3 2 1 0 13 12 11 10 9 8 7 20 19 18 17 16 15 ...
7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 23 22 21 20 ...
8 7 6 5 4 3 2 1 0 17 16 15 14 13 12 11 10 9 26 25 ...
9 8 7 6 5 4 3 2 1 0 19 18 17 16 15 14 13 12 11 10 ......
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MAPLE
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a:= (n, w) -> ((w - (n mod w) - 1) + n) - (n mod w):
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PROG
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(PARI) a(n, w) = ((w - n % w - 1) + n) - n % w;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Entry revised by Editors of the OEIS, Jun 17 2023
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STATUS
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approved
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