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A373034
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Triangle read by rows: T(n,k) is the number of edge subsets E of the n-dimensional hypercube graph such that E contains a path between two given nodes at Hamming distance k, 0 <= k <= n.
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2
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1, 2, 1, 16, 9, 7, 4096, 2703, 2334, 2160, 4294967296, 3425712321, 3245350248, 3170502909, 3127853061
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OFFSET
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0,2
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COMMENTS
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T(n,k)/A061301(n) is the probability that two given nodes at Hamming distance k in the n-dimensional hypercube graph are still connected after each edge has been independently deleted with probability 1/2.
The bunkbed conjecture holds for the n-dimensional hypercube graph with edge-probability 1/2 if and only if the (n+1)-st row is nonincreasing.
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LINKS
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EXAMPLE
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Triangle begins:
1;
2, 1;
16, 9, 7;
4096, 2703, 2334, 2160;
4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
...
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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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