%I #10 Nov 02 2024 11:51:19
%S 1,2,1,16,9,7,4096,2703,2334,2160,4294967296,3425712321,3245350248,
%T 3170502909,3127853061
%N 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.
%C 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.
%C 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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bunkbed_conjecture">Bunkbed conjecture</a>.
%e Triangle begins:
%e 1;
%e 2, 1;
%e 16, 9, 7;
%e 4096, 2703, 2334, 2160;
%e 4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
%e ...
%Y Cf. A061301 (first column), A372705, A373035 (main diagonal).
%K nonn,tabl,more
%O 0,2
%A _Pontus von Brömssen_, May 20 2024