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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. 0
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".

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. [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]

LINKS

Table of n, a(n) for n=1..10.

PDF version of "Coin-Moving Puzzles" [From John Tromp, Nov 05 2008]

Science News article [From John Tromp, Nov 05 2008]

EXAMPLE

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.

CROSSREFS

Sequence in context: A168658 A235347 A235352 * A246481 A048990 A089602

Adjacent sequences:  A146968 A146969 A146970 * A146972 A146973 A146974

KEYWORD

nonn

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(1) 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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Last modified February 21 19:26 EST 2018. Contains 299422 sequences. (Running on oeis4.)