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A007016 Number of permutations of length n with 1 fixed and 1 reflected point.
(Formerly M4491)
+0
2
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)
OFFSET

0,5

COMMENT

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.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Simpson, Todd; Permutations with unique fixed and reflected points. Ars Combin. 39 (1995), 97-108.

FORMULA

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).

CROSSREFS

Sequence in context: A101363 A003685 A066011 this_sequence A129550 A014584 A074472

Adjacent sequences: A007013 A007014 A007015 this_sequence A007017 A007018 A007019

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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