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A373036
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Triangle read by rows: T(n,k) is the number of edge subsets E of the n X k grid graph such that E contains a path between the top left node and the bottom right node, 1 <= k <= n.
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5
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1, 1, 7, 1, 40, 1135, 1, 216, 28942, 3329245, 1, 1144, 707239, 358911148, 167176484530, 1, 6016, 16963938, 37502829018, 74568672196498, 140386491543732211, 1, 31552, 403490839, 3856945416544, 32485805235240376, 256258754970108999490, 1946586793700869420041631
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OFFSET
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1,3
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COMMENTS
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T(n,k)/2^A151890(n-1,k-1) is the probability that the top left and bottom right vertices of the n X k grid graph are still connected after each edge has been independently deleted with probability 1/2.
Terms in the n-th row/column satisfies a linear recurrence with constant coefficients (probably of order A000245(n) or less).
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 7;
1, 40, 1135;
1, 216, 28942, 3329245;
1, 1144, 707239, 358911148, 167176484530;
1, 6016, 16963938, 37502829018, 74568672196498, 140386491543732211;
...
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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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