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 A146971 Number of weight-n binary n X n matrices that yield the all-ones matrix after repeatedly changing a 0 having at least two 1-neighbors to a 1. 3
 1, 2, 14, 130, 1615, 23140, 383820, 7006916, 140537609, 3035127766 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There is a proof that the minimum initial weight is n which can be summarized in the single word "perimeter". Can also be described as the number of percolating sets of size n for 2-neighbor bootstrap percolation in the n X n grid graph; see Balogh, Bollobás and Morris. The large Schröder numbers A006318 count the permutation matrices (one 1 in each row and column) having this property. - Jonathan Noel, Oct 07 2018 REFERENCES Erik D. Demaine, Martin L. Demaine and Helena A. Verrill, "Coin-Moving Puzzles", in More Games of No Chance, edited by R. J. Nowakowski, 2002, pages 405-431, Cambridge University Press. Collection of papers from the MSRI Combinatorial Game Theory Research Workshop, Berkeley, California, July 24-28, 2000. LINKS Table of n, a(n) for n=1..10. József Balogh, Béla Bollobás and Robert Morris, Bootstrap percolation in high dimensions, arXiv:0907.3097 [math.PR], 2009-2010. József Balogh, Béla Bollobás and Robert Morris, Bootstrap percolation in high dimensions, Combin. Probab. Comput. 19 (2010), no. 5-6, 643-692. Michael S. Branicky, Python program. Erik D. Demaine, Martin L. Demaine and Helena A. Verrill, , PDF version of "Coin-Moving Puzzles" Ivars Peterson, Sliding-Coin Puzzles, Science News 163(5), Feb 01, 2003. Description of results in the above paper. EXAMPLE a(3) = 14 because there are 2, 4, 4 and 4 symmetrical versions of 100 010 001, 100 001 010, 101 000 100 and 101 000 010 respectively. PROG (Python) # see linked program CROSSREFS Sequence in context: A168658 A235347 A235352 * A246481 A048990 A089602 Adjacent sequences: A146968 A146969 A146970 * A146972 A146973 A146974 KEYWORD nonn,more AUTHOR John Tromp, Nov 03 2008 EXTENSIONS Additional term a(8) from Alvaro Begue's C-program. - John Tromp, Nov 05 2008 Computed a(9) and a(10) with a 128-bitboard based program, the former verifying a result from Alvaro's array based program. - John Tromp, Nov 20 2008 STATUS approved

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