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A279445
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Triangle read by rows: T(n, k) is the number of ways to place k points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.
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10
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1, 1, 1, 4, 6, 4, 1, 1, 9, 36, 78, 90, 45, 6, 1, 16, 120, 528, 1428, 2304, 2040, 816, 90, 1, 25, 300, 2200, 10600, 34020, 71400, 93000, 67950, 22650, 2040, 1, 36, 630, 6900, 51525, 270720, 1005720, 2602800, 4531950, 4987800, 3110940, 888840, 67950, 1, 49, 1176, 17934
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OFFSET
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1,4
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COMMENTS
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Length of n-th row is A272651(n) + 1, where A272651(n) is the maximal number of points to be placed under the condition mentioned.
Rotations and reflections of placements are counted. If they are to be ignored, see A279453.
For condition "no more than 2 points on a straight line at any angle", see A194193 (but that one is read by antidiagonals).
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LINKS
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Heinrich Ludwig, Table of n, a(n) for n = 1..109
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EXAMPLE
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The table begins with T(1, 0):
1 1
1 4 6 4 1
1 9 36 78 90 45 6
1 16 120 528 1428 2304 2040 816 90
1 25 300 2200 10600 34020 71400 93000 67950 22650 2040
...
T(3, 2) = 36 because there are 36 ways to place 2 points on a 3 X 3 square grid so that no more than 2 points are on a vertical or horizontal straight line.
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CROSSREFS
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Row sums give A197458.
Columns 2..10: A000290, A083374, A279437, A279438, A279439, A279440, A279441, A279442, A279443.
Diagonal T(n, n) is A279444.
Cf. A279453, A194193.
Sequence in context: A230207 A277949 A244081 * A217285 A212635 A087108
Adjacent sequences: A279442 A279443 A279444 * A279446 A279447 A279448
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KEYWORD
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nonn,tabf
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AUTHOR
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Heinrich Ludwig, Dec 17 2016
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STATUS
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approved
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