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A373034
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.
2
1, 2, 1, 16, 9, 7, 4096, 2703, 2334, 2160, 4294967296, 3425712321, 3245350248, 3170502909, 3127853061
OFFSET
0,2
COMMENTS
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 (the version where all edges, including the posts, have the same probability 1/2 of being retained) holds for the n-dimensional hypercube graph if and only if the (n+1)-st row is nonincreasing.
EXAMPLE
Triangle begins:
1;
2, 1;
16, 9, 7;
4096, 2703, 2334, 2160;
4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
...
CROSSREFS
Cf. A061301 (first column), A372705, A373035 (main diagonal).
Sequence in context: A016447 A095850 A324610 * A247125 A290315 A113108
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved