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A086266, and A086268
in "The On-Line Encyclopedia of Integer Sequences."Temperley,
H. N. V. and Lieb, E. H. "Relations Between the 'Percolation'
and 'Colouring' Problem and Other Graph-Theoretical Problems Associated with Regular
Planar Lattices; Some Exact Results for the 'Percolation' Problem." Proc.
Roy. Soc. London A322, 251-280, 1971.Ziff, R. M.; Finch,
S. R.; and Adamchik, V. S. "Universality of Finite-Size Corrections
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3447-3450, 1997. https://doi.org/10.1103/PhysRevLett.79.3447.
-cluster in a random 
(0,1)-matrix whose entries
independently equal 1 (with probability 
) or 0 (with probability 
) is a connected
component of 
1s, using horizontal or vertical nearest-neighbor adjacency. Here 
and 
are positive integers and 
. The numbers of 
(0,1)-matrices with 
site clusters for 
, 1, ... are summarized in the following table (OEIS A086266).
, 1, ... clusters
, this gives the mean
total numbers of site clusters for 
, 2, ... as 1/2, 17/16, 897/512, 168529/65536, ... (numerators
OEIS A086265).
be the total number of clusters
in this site percolation model. Then the value
is the expectation
value of 
.
Numerically, it is found that
