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A350819
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Array read by antidiagonals: T(m,n) is the number of maximum independent sets in the 2m X 2n king graph.
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14
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1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 32, 79, 32, 1, 1, 80, 408, 408, 80, 1, 1, 192, 1847, 3600, 1847, 192, 1, 1, 448, 7698, 26040, 26040, 7698, 448, 1, 1, 1024, 30319, 166368, 281571, 166368, 30319, 1024, 1, 1, 2304, 114606, 976640, 2580754, 2580754, 976640, 114606, 2304, 1
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OFFSET
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0,5
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COMMENTS
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Number of ways to tile a (2m+1) X (2n+1) board with m*n 2 X 2 tiles and 2m+2n+1 1 X 1 tiles.
For m,n > 0, T(m,n) is the number of minimum dominating sets in the (3m-1) X (3n-1) king graph.
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LINKS
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FORMULA
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T(m,n) = T(n,m).
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EXAMPLE
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Table begins:
=============================================
m\n | 0 1 2 3 4 5
----+----------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 1 4 12 32 80 192 ...
2 | 1 12 79 408 1847 7698 ...
3 | 1 32 408 3600 26040 166368 ...
4 | 1 80 1847 26040 281571 2580754 ...
5 | 1 192 7698 166368 2580754 32572756 ...
...
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CROSSREFS
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Rows 0..12 are A000012, A001787(n+1), A061593, A061594, A173782, A173783, A174154, A174155, A174558, A195648, A195649, A195650, A195651.
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KEYWORD
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AUTHOR
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STATUS
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approved
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