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%I #11 Oct 12 2023 19:25:42
%S 0,0,4,4,1,0,0,0,0,4,48,272,944,2214,3696,4408,3536,1768,560,120,16,1,
%T 0,0,0,0,0,0,462,12456,162810,1370172,8316297,38643624,142444695,
%U 426043278,1049742000,2153912760,3711426624,5409742482,6716638430,7153883766,6584406876,5274811392,3701882250,2287146006,1247224353,600206400,254134359,94140796,30260304,8347680,1947792,376992,58905,7140,630,36,1
%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 either dimension.
%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, 4, 4, 1,
%e 0, 0, 0, 0, 4, 48, 272, 944, 2214, 3696, 4408, 3536, 1768, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 0, 462, 12456, 162810, 1370172, 8316297, 38643624, 142444695, 426043278, 1049742000, 2153912760, 3711426624, 5409742482, 6716638430, 7153883766, 6584406876, 5274811392, 3701882250, 2287146006, 1247224353, 600206400, 254134359, 94140796, 30260304, 8347680, 1947792, 376992, 58905, 7140, 630, 36, 1,
%e ...
%Y Cf. A365940-A365956, A366463-A366467.
%K nonn,tabf
%O 1,3
%A _N. J. A. Sloane_, Oct 12 2023
%E The DATA shows three rows of the triangle.