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%I #11 Oct 12 2023 19:24:03
%S 0,0,0,4,1,0,0,0,0,0,0,0,0,4,32,160,448,588,352,104,16,1,0,0,0,0,0,0,
%T 6,180,3186,38832,343125,2284920,11812665,48453246,160204284,
%U 432061500,959302998,1766890134,2717497054,3511031418,3832283250,3552960132,2812344534,1909555974,1116592323,563847696,246161187,92809456,30100680,8335404,1947336,376992,58905,7140,630,36,1
%N Irregular triangle read by rows: T(N,k) (0 <= k <= 4*N^2) are coefficients of exact wrapping probability for site percolation on a 2*N X 2*N 2D hexagonal lattice with periodic boundary conditions. This is for the probability that it wraps in both dimensions.
%C The wrapping probability function is Sum_{k=0..4*N^2} T(N,k)*p^k*(1-p)^(4*N^2-k).
%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a>
%e Triangle begins:
%e 0, 0, 0, 4, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 4, 32, 160, 448, 588, 352, 104, 16, 1,
%e 0, 0, 0, 0, 0, 0, 6, 180, 3186, 38832, 343125, 2284920, 11812665, 48453246, 160204284, 432061500, 959302998, 1766890134, 2717497054, 3511031418, 3832283250, 3552960132, 2812344534, 1909555974, 1116592323, 563847696, 246161187, 92809456, 30100680, 8335404, 1947336, 376992, 58905, 7140, 630, 36, 1,
%e ...
%Y Cf. A365940-A365957, A366463-A366467.
%K nonn,tabf
%O 1,4
%A _N. J. A. Sloane_, Oct 12 2023
%E The DATA shows three rows of the triangle.
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