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.

1, 2, 1, 16, 9, 7, 4096, 2703, 2334, 2160, 4294967296, 3425712321, 3245350248, 3170502909, 3127853061

Offset: 0

Author

Pontus von Brömssen, May 20 2024

Keywords

• nonn
• tabl
• more

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.

Examples

			Triangle begins:
           1;
           2,          1;
          16,          9,          7;
        4096,       2703,       2334,       2160;
  4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
  ...
		

Links

• Wikipedia, Bunkbed conjecture.

Crossrefs

Cf. A061301 (first column), A372705, A373035 (main diagonal).