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 A320212 Number of binary n X n X n permutation arrays (all projections onto 2-dimensional faces yield the all-ones matrix) which yield the all-ones array when repeatedly changing a 0 with three 1 neighbors to 1. 0
 1, 2, 12, 256, 26888, 148958 (list; graph; refs; listen; history; text; internal format)
 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 3-neighbor 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 2-neighbor bootstrap percolation is enumerated by the Large Schröder numbers A006318. See Shapiro and Stephens (1991). LINKS Table of n, a(n) for n=1..6. József Balogh, Béla Bollobás and Robert Morris, Bootstrap percolation in three dimensions, Ann. Probab. 37 (2009), no. 4, 1329-1380. L. Shapiro and A. B. Stephens, Bootstrap percolation, the Schröder numbers and the N-kings problem, SIAM J. Discrete Math., Vol. 4 (1991), pp. 275-280. 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 (n-1)!n! arrays that are obtained from this example by permuting rows and columns. For larger n, more complicated examples exist. CROSSREFS Cf. A006318, A146971. Sequence in context: A132481 A369680 A217652 * A361749 A012549 A009610 Adjacent sequences: A320209 A320210 A320211 * A320213 A320214 A320215 KEYWORD nonn,more AUTHOR Jonathan Noel, Oct 07 2018 STATUS approved

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Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)