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A366464
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Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact wrapping probability for site percolation on an n X n 2D nnsquare lattice with periodic boundary conditions. This is for the probability that it wraps around the vertical dimension.
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1
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0, 1, 0, 0, 4, 4, 1, 0, 0, 0, 27, 81, 108, 81, 36, 9, 1, 0, 0, 0, 0, 84, 832, 3368, 7376, 10432, 10432, 7728, 4320, 1816, 560, 120, 16, 1, 0, 0, 0, 0, 0, 265, 4675, 39300, 201000, 687425, 1660325, 2970175, 4114225, 4569025, 4165275, 3161975, 2012650, 1075075, 479700, 177000, 53125, 12650, 2300, 300, 25, 1
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OFFSET
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1,5
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COMMENTS
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An nnsquare lattice is a square lattice with additional next nearest neighbor links.
The wrapping probability function is Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
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LINKS
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EXAMPLE
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Triangle begins:
0, 1,
0, 0, 4, 4, 1,
0, 0, 0, 27, 81, 108, 81, 36, 9, 1,
0, 0, 0, 0, 84, 832, 3368, 7376, 10432, 10432, 7728, 4320, 1816, 560, 120, 16, 1,
0, 0, 0, 0, 0, 265, 4675, 39300, 201000, 687425, 1660325, 2970175, 4114225, 4569025, 4165275, 3161975, 2012650, 1075075, 479700, 177000, 53125, 12650, 2300, 300, 25, 1,
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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