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%I #13 Oct 11 2023 03:55:27
%S 0,1,0,4,6,4,1,0,9,52,128,177,154,90,36,9,1,0,16,198,1128,3921,9296,
%T 15932,20452,20168,15600,9628,4776,1880,564,120,16,1,0,25,528,5308,
%U 33785,152766,521962,1399532,3019536,5334899,7819026,9603688,9971750,8823881,6704598,4401190,2503378,1230980,518728,184464,54156,12742,2304,300,25,1
%N Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of cluster density function for site percolation on an n X n 2D nnsquare lattice with open boundary conditions.
%C An nnsquare lattice is a square lattice with additional next nearest neighbor links.
%C The cluster density function is (1/n^2)*Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a> (Gives first 16 rows)
%e Triangle begins:
%e 0, 1,
%e 0, 4, 6, 4, 1,
%e 0, 9, 52, 128, 177, 154, 90, 36, 9, 1,
%e 0, 16, 198, 1128, 3921, 9296, 15932, 20452, 20168, 15600, 9628, 4776, 1880, 564, 120, 16, 1,
%e 0, 25, 528, 5308, 33785, 152766, 521962, 1399532, 3019536, 5334899, 7819026, 9603688, 9971750, 8823881, 6704598, 4401190, 2503378, 1230980, 518728, 184464, 54156, 12742, 2304, 300, 25, 1,
%e ...
%Y Cf. A365940-A365946.
%K nonn,tabf
%O 1,4
%A _N. J. A. Sloane_, Oct 10 2023
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