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A292153
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Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square grid such that the picked positions have a point symmetry or a line symmetry.
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9
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1, 4, 6, 9, 36, 44, 16, 120, 192, 388, 25, 300, 596, 1658, 2138, 36, 630, 1436, 5121, 7216, 22328, 49, 1176, 3024, 13180, 21756, 80192, 126616, 64, 2016, 5568, 29112, 51616, 230784, 394504, 1409328
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OFFSET
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1,2
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COMMENTS
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The "or" is inclusive, i.e. configurations that have both types of symmetry simultaneously (counted separately in A292154) are included.
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LINKS
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FORMULA
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EXAMPLE
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The triangle begins:
1;
4, 6;
9, 36, 44;
16, 120, 192, 388;
25, 300, 596, 1658, 2138;
36, 630, 1436, 5121, 7216, 22328;
49, 1176, 3024, 13180, 21756, 80192, 126616;
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The following configuration is one of the T(4,3)=a(9)=192 symmetric configurations of 3 points picked from a 4 X 4 grid. It has both types of symmetry.
0 0 0 0
X 0 0 0
0 X 0 0
0 0 X 0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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