cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A373034 #10 Nov 02 2024 11:51:19
%S A373034 1,2,1,16,9,7,4096,2703,2334,2160,4294967296,3425712321,3245350248,
%T A373034 3170502909,3127853061
%N 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.
%C A373034 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 A373034 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 A373034 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bunkbed_conjecture">Bunkbed conjecture</a>.
%e A373034 Triangle begins:
%e A373034            1;
%e A373034            2,          1;
%e A373034           16,          9,          7;
%e A373034         4096,       2703,       2334,       2160;
%e A373034   4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
%e A373034   ...
%Y A373034 Cf. A061301 (first column), A372705, A373035 (main diagonal).
%K A373034 nonn,tabl,more
%O A373034 0,2
%A A373034 _Pontus von Brömssen_, May 20 2024