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A308178
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Scan an infinite 45-degree triangular chessboard (cells (x,y) with 0 <= y <= x) by upwards antidiagonals, filling in each cell with the smallest nonnegative number already placed that cannot be seen by a chess queen at (x,y); sequence gives numbers along the successive antidiagonals.
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3
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0, 1, 2, 3, 3, 0, 4, 1, 5, 5, 2, 4, 6, 7, 0, 2, 7, 4, 1, 3, 8, 5, 2, 4, 1, 9, 6, 3, 0, 2, 10, 11, 7, 1, 3, 6, 11, 8, 10, 9, 4, 5, 12, 9, 6, 8, 0, 10, 7, 13, 10, 12, 5, 6, 11, 8, 14, 15, 8, 7, 9, 3, 5, 11, 15, 12, 9, 6, 8, 0, 13, 10, 16, 13, 11, 12, 5, 1, 14, 7
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OFFSET
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0,3
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COMMENTS
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The 0's occur in positions (x,y) = (2k,k), k >= 0.
After 13 steps, the y=2 column appears to become quasi-periodic with a saltus of 4. That is, the first differences appear to become periodic with period (-1, -2, 1, 6).
There is a very similar triangle in A274650.
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LINKS
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EXAMPLE
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Start of chessboard showing antidiagonals 0 through 12:
y = 0, 1, 2, 3, 4, 5, 6, 7, ...
--------------------------------
x=0 0,
x=1 1, 3,
x=2 2, 0, 5,
x=3 3, 1, 4, 2,
x=4 4, 2, 0, 3, 1,
x=5 5, 7, 1, 4, 2, 6,
x=6 6, 4, 2, 0, 3, 5, 7,
x=7 7, 5, 3, 1, 4, 10, ...,
x=8 8, 6, 7, 9, 0, ...,
x=9 9, 11, 10, 8, ...,
x=10 10, 8, 6, ...,
x=11 11, 9, ...,
x=12 12, ...,
x=13 ...,
The first few antidiagonals are:
0,
1,
2, 3,
3, 0,
4, 1, 5,
5, 2, 4,
6, 7, 0, 2,
7, 4, 1, 3,
8, 5, 2, 4, 1,
9, 6, 3, 0, 2,
...
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PROG
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(PARI) See Links section.
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CROSSREFS
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Reading the triangle across rows gives A308179.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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