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A288187
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Triangle read by rows: T(n,m) (n >= m >= 1) = number of chambers (or regions) formed by drawing the line segments connecting any two of the (n+1) X (m+1) lattice points in an n X m lattice polygon.
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16
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4, 16, 56, 46, 176, 520, 104, 388, 1152, 2584, 214, 822, 2502, 5700, 12368, 380, 1452, 4392, 9944, 21504, 37400, 648, 2516, 7644, 17380, 37572, 65810, 115532, 1028, 3952, 12120, 27572, 59784, 105128, 184442, 294040, 1562, 6060, 18476, 42066, 91654, 161352, 282754, 450864, 690816
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OFFSET
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1,1
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COMMENTS
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Chambers are counted regardless of their numbers of vertices.
The n X m lattice polygon mentioned in the definition is an n X m grid of square cells, formed using a grid of n+1 X m+1 points. - N. J. A. Sloane, Feb 07 2019
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LINKS
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EXAMPLE
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The diagonals of the 1 X 1 lattice polygon, i.e. the square, cut it into 4 triangles. Therefore T(1,1)=4.
Triangle begins
4,
16, 56,
46, 176, 520,
104, 388, 1152, 2584,
214, 822, 2502, 5700, 12368,
...
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CROSSREFS
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If the initial points are arranged around a circle rather than a square we get A006533 and A007678.
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KEYWORD
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AUTHOR
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EXTENSIONS
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T(3,3) corrected and rows for n=4..9 added by Max Alekseyev, Apr 05 2019.
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STATUS
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approved
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