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%I A365956 #13 Oct 12 2023 19:25:14
%S A365956 0,0,6,4,1,0,0,0,0,68,640,2644,6320,9773,10304,7788,4352,1820,560,120,
%T A365956 16,1,0,0,0,0,0,0,462,12456,162810,1370172,8316297,38643624,142444695,
%U A365956 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 A365956 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 union jack lattice with periodic boundary conditions. This is for the probability that it wraps in either dimension.
%C A365956 The wrapping probability function is Sum_{k=0..4*N^2} T(N,k)*p^k*(1-p)^(4*N^2-k).
%H A365956 Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a>
%e A365956 Triangle begins:
%e A365956   0, 0, 6, 4, 1,
%e A365956   0, 0, 0, 0, 68, 640, 2644, 6320, 9773, 10304, 7788, 4352, 1820, 560, 120, 16, 1,
%e A365956   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 A365956 ...
%Y A365956 Cf. A365940-A365957, A366463-A366467.
%K A365956 nonn,tabf
%O A365956 1,3
%A A365956 _N. J. A. Sloane_, Oct 12 2023
%E A365956 The DATA shows three rows of the triangle.

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