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A054417
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Number of connected 3 X n binary matrices with rightmost column [1,0,0]'.
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5
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1, 5, 37, 249, 1657, 11037, 73533, 489905, 3263921, 21745397, 144875541, 965212201, 6430585769, 42842841485, 285434194093, 1901663763041, 12669557966433, 84409085446373, 562363243040517, 3746663234776665
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OFFSET
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1,2
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COMMENTS
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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.
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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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LINKS
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FORMULA
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a(n)=7*a(n-1)-3*a(n-2)+5*a(n-3).
G.f.: x*(1-2*x+5*x^2)/(1-7*x+3*x^2-5*x^3). [Colin Barker, Mar 08 2012]
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MATHEMATICA
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CoefficientList[Series[(1-2*x+5*x^2)/(1-7*x+3*x^2-5*x^3), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2012 *)
LinearRecurrence[{7, -3, 5}, {1, 5, 37}, 20] (* Harvey P. Dale, Jan 29 2014 *)
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PROG
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(Magma) I:=[1, 5, 37]; [n le 3 select I[n] else 7*Self(n-1)-3*Self(n-2)+5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 28 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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