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A054421
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Number of disconnected 3 X n binary matrices.
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5
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0, 1, 11, 102, 882, 7295, 58533, 459484, 3547860, 27043405, 204016879, 1526141666, 11336059046, 83703379691, 614911337833, 4497505562616, 32769214114664, 237956784843737, 1722809101653651, 12440161483566494, 89616141395864986, 644202131570116247
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OFFSET
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1,3
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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. 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) = 14*a(n-1)-52*a(n-2)+26*a(n-3)-35*a(n-4). G.f.: -x^2*(3*x-1) / ((7*x-1)*(5*x^3-3*x^2+7*x-1)). - Colin Barker, Jan 13 2014
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PROG
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(PARI) Vec(-x^2*(3*x-1)/((7*x-1)*(5*x^3-3*x^2+7*x-1)) + O(x^100)) \\ Colin Barker, Jan 13 2014
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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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