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A146971 Number of weight-n binary n X n matrices that yield the all-1 matrix when repeatedly change a 0 having at least two 1-neighbors to a 1. 2
1, 2, 14, 130, 1615, 23140, 383820, 7006916, 140537609, 3035127766 (list; graph; refs; listen; history; text; internal format)



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-neighbour bootstrap percolation in the n X n grid graph; see Balogh, Bollobás and Morris. The large Schröder numbers A006318 count the number of permutation matrices (one 1 in each row and column) having this property. - Jonathan Noel, Oct 07 2018


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. [From John Tromp, Nov 05 2008]

Ivars Peterson, "Sliding-Coin Puzzles", Science News 163(5), Feb 01, 2003 (description of results in the above paper) [From John Tromp, Nov 05 2008]

József Balogh, Béla  Bollobás and Robert Morris, "Bootstrap percolation in high dimensions," Combin. Probab. Comput. 19 (2010), no. 5-6, 643-692.


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.

Erik D. Demaine, Martin L. Demaine and Helena A. Verrill, , PDF version of "Coin-Moving Puzzles" [From John Tromp, Nov 05 2008]

Ivars Peterson, Sliding-Coin Puzzles [From John Tromp, Nov 05 2008]


a(3) = 14 because of there are 2,4,4 and 4 symmetrical versions of 100 010 001, 100 001 010, 101 000 100 and 101 000 010 respectively.


Sequence in context: A168658 A235347 A235352 * A246481 A048990 A089602

Adjacent sequences:  A146968 A146969 A146970 * A146972 A146973 A146974




John Tromp, Nov 03 2008


Additional term a(8) from Alvaro Begue's C-program. John Tromp, Nov 05 2008

Computed a(9) and a(1) with a 128-bitboard based program, the former verifying a result from Alvaro's array based program. John Tromp, Nov 20 2008



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Last modified October 23 01:57 EDT 2018. Contains 316518 sequences. (Running on oeis4.)