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A362977
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The x-coordinates of the even-ranked elements of the lexicographically earliest sequence of points satisfying staircase and no-three-in-a-line conditions (see comments).
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2
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0, 1, 2, 5, 6, 3, 12, 13, 4, 15, 8, 27, 19, 11, 9, 32, 25, 16, 33, 35, 59, 30, 24, 7, 51, 45, 10, 18, 29, 26, 54, 58, 14, 53, 23, 34, 37, 49, 44, 60, 43, 31, 41, 66, 17, 72, 80, 81, 78, 88, 87, 46, 83, 22, 76, 79, 130, 97, 108, 111, 94, 119, 153, 89, 39, 112
(list;
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refs;
listen;
history;
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OFFSET
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0,3
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COMMENTS
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We construct the lexicographically earliest sequence of points M(i), for i >= 0, with the following rules:
- their (x, y) coordinates are taken among the nonnegative integers;
- if i > 0 and i is odd, then "move horizontally to a free column"; i.e., M(i) must have the same y as M(i-1), and M(i) is not allowed to have the same x as any M(k) for k < i;
- if i > 0 and i is even, then "move vertically to a free row"; i.e., M(i) must have the same x as M(i-1), and M(i) is not allowed to have the same y as any M(k) for k < i;
- three points are not allowed to be aligned.
See SVG illustration, Links section.
Then a(n) (resp. A362978(n)) is defined as the x-coordinate (resp. y-coordinate) of M(i), where i := 2n (to eliminate duplicates).
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LINKS
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EXAMPLE
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y
^
| . . . 9 . . 8
| . . 4 . . 5 .
| . . . . . 6 7
| . 2 3 . . . .
| 0 1 . . . . .
+-------------------> x
0 1 2 3 4 5 6
Abscissas of the points 0, 2, 4, 6, 8, ...: 0, 1, 2, 5, 6, ...
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PROG
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(Java) see link.
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CROSSREFS
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Cf. A362978 (the corresponding y-coordinates).
Cf. A161680 (number of nonalignment checks to pass).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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