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Search: id:A054420
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| A054420 |
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Number of connectable 3 X n binary matrices. |
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+0
2
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| 1, 3, 13, 87, 585, 3899, 25973, 173039, 1152849, 7680691, 51171485, 340922567, 2271346969, 15132518507, 100818201477, 671686589663, 4475014115745, 29814130048611, 198632300941357, 1323358787022391, 8816685256575721
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A connected (0,1) matrix is one where you can get from any black square, i.e. a 1, to any other by chess king moves. A matrix is connectable if it is not connected, has rightmost column [1,0,1]', and becomes connected when any of [1,1,1]', [1,1,0]', [0,1,1]' or [0,1,0]' is appended.
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REFERENCES
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R. Levy and J. Shapiro, Uniqueness in paint-by-numbers puzzles, preprint, 2000.
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FORMULA
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a(n)=7a(n-1)-3a(n-2)+5a(n-3).
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CROSSREFS
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Cf. A054417-A054421. A054420(n) = A054421(n-1) + 2*A054418(n-1).
Sequence in context: A125500 A121679 A023037 this_sequence A001831 A002725 A097711
Adjacent sequences: A054417 A054418 A054419 this_sequence A054421 A054422 A054423
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KEYWORD
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nonn
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AUTHOR
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njas, May 22 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 23 2000
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