

A320212


Number of binary n X n X n permutation arrays (all projections onto 2dimensional faces yield the allones matrix) which yield the allones array when repeatedly changing a 0 with three 1 neighbors to 1.


0




OFFSET

1,2


COMMENTS

This can be phrased as the number of n X n X n permutation arrays which percolate with respect to the 3neighbor bootstrap percolation rule in the n X n X n grid. C.f. Balogh, Bollobás and Morris (2009).
The analogous sequence for n X n permutation arrays with respect to 2neighbor bootstrap percolation is enumerated by the Large Schröder numbers A006318. See Shapiro and Stephens (1991).


LINKS



EXAMPLE

One example of such an array is the n X n X n array in which the (i,j,k) entry is 1 if i+j+k is 0 mod n. For n=2 and n=3, the arrays counted by a(n) are precisely the (n1)!n! arrays that are obtained from this example by permuting rows and columns. For larger n, more complicated examples exist.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



