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Search: id:A146971
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| A146971 |
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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-neighbours to a 1. |
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+0
1
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| 1, 2, 14, 130, 1615, 23140, 383820, 7006916, 140537609, 3035127766
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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There is a proof that the minimum initial weight is n which can be summarized in the single word "perimeter".
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REFERENCES
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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 (john.tromp(AT)gmail.com), 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 (john.tromp(AT)gmail.com), Nov 05 2008]
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LINKS
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PDF version of "Coin-Moving Puzzles" [From John Tromp (john.tromp(AT)gmail.com), Nov 05 2008]
Science News article [From John Tromp (john.tromp(AT)gmail.com), Nov 05 2008]
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A060468 A121082 A155650 this_sequence A048990 A089602 A052641
Adjacent sequences: A146968 A146969 A146970 this_sequence A146972 A146973 A146974
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KEYWORD
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nonn
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AUTHOR
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John Tromp (john.tromp(AT)gmail.com), Nov 03 2008
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EXTENSIONS
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Additional term a(8) from Alvaro Begue's C-program. John Tromp (john.tromp(AT)gmail.com), 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 (john.tromp(AT)gmail.com), Nov 20 2008
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