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A360916
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Array read by antidiagonals: T(m,n) is the number of maximum induced paths in the grid graph P_m X P_n.
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6
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1, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 6, 8, 6, 1, 1, 2, 14, 14, 2, 1, 1, 8, 18, 84, 18, 8, 1, 1, 2, 2, 26, 26, 2, 2, 1, 1, 10, 4, 32, 56, 32, 4, 10, 1, 1, 2, 6, 16, 4, 4, 16, 6, 2, 1, 1, 12, 8, 152, 24, 136, 24, 152, 8, 12, 1, 1, 2, 10, 48, 32, 10, 10, 32, 48, 10, 2, 1
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OFFSET
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1,5
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COMMENTS
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A maximum induced path is an induced path of longest length.
T(m,n) is the number of snake-like polyominoes with the maximum possible number of unit squares in an m X n rectangle.
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LINKS
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Eric Weisstein's World of Mathematics, Grid Graph.
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FORMULA
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T(m,n) = T(n,m).
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EXAMPLE
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Array begins:
========================================
m\n| 1 2 3 4 5 6 7 8 9 ...
---+------------------------------------
1 | 1 1 1 1 1 1 1 1 1 ...
2 | 1 4 2 6 2 8 2 10 2 ...
3 | 1 2 8 14 18 2 4 6 8 ...
4 | 1 6 14 84 26 32 16 152 48 ...
5 | 1 2 18 26 56 4 24 32 108 ...
6 | 1 8 2 32 4 136 10 168 32 ...
7 | 1 2 4 16 24 10 52 4 8 ...
8 | 1 10 6 152 32 168 4 216 8 ...
9 | 1 2 8 48 108 32 8 8 16 ...
...
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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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