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%I #11 Oct 09 2023 20:44:25
%S 0,1,0,4,6,4,1,0,9,36,84,126,126,84,36,9,1,0,16,176,848,2448,5056,
%T 8440,11584,12890,11440,8008,4368,1820,560,120,16,1,0,25,500,4700,
%U 27500,112145,339650,801500,1543750,2538800,3675220,4717300,5330625,5250975,4472200,3271820,2043375,1081600,480700,177100,53130,12650,2300,300,25,1
%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 periodic 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).
%D S. Mertens, I. Jensen, and R. M. Ziff, Universal features of cluster numbers in percolation, Physical Review E 96 (2017) 052119.
%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a> (Gives first 7 rows)
%e Triangle begins:
%e 0, 1,
%e 0, 4, 6, 4, 1,
%e 0, 9, 36, 84, 126, 126, 84, 36, 9, 1,
%e 0, 16, 176, 848, 2448, 5056, 8440, 11584, 12890, 11440, 8008, 4368, 1820, 560, 120, 16, 1,
%e ...
%Y Cf. A365940-A365944.
%K nonn,tabf
%O 1,4
%A _N. J. A. Sloane_, Oct 09 2023
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