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Search: id:A007016
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| A007016 |
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Number of permutations of length n with 1 fixed and 1 reflected point.
(Formerly M4491)
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+0
2
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| 0, 1, 0, 0, 8, 20, 96, 656, 5568, 48912, 494080, 5383552, 65097600, 840566080, 11833898496, 176621049600, 2838024476672, 48060623405312, 868000333234176, 16441638519762944, 329723762151352320, 6907027877807330304
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of distinct solutions to the order n checkerboard problem, including symmetrical solutions: place n pieces on an n X n board so there is exactly one piece in each row, column, and main diagonal. Compare A064280.
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REFERENCES
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Simpson, Todd; Permutations with unique fixed and reflected points. Ars Combin. 39 (1995), 97-108.
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FORMULA
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a(2*m) = m*(x(2*m) - (2*m-3)*x(2*m-1)), a(2*m+1) = (2*m+1)*x(2*m) + 3*m*x(2*m-1) - 2*m*(m-1)*x(2*m-2), where x(n) = A003471(n).
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CROSSREFS
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Sequence in context: A101363 A003685 A066011 this_sequence A129550 A014584 A074472
Adjacent sequences: A007013 A007014 A007015 this_sequence A007017 A007018 A007019
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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