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A215287
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Number of permutations of 0..floor((n*3-1)/2) on even squares of an n X 3 array such that each row and column of even squares is increasing.
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2
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1, 3, 10, 30, 140, 420, 2310, 6930, 42042, 126126, 816816, 2450448, 16628040, 49884120, 350574510, 1051723530, 7595781050, 22787343150, 168212023980, 504636071940, 3792416540640, 11377249621920, 86787993910800, 260363981732400, 2011383287449200
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OFFSET
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1,2
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COMMENTS
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Also Schröder paths of length n having floor(n/2) peaks. - Peter Luschny, Sep 30 2018
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LINKS
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FORMULA
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f3 = floor((n+1)/2); f4 = floor(n/2);
a(n) = (n - f + 1)*(2*n - f)! / ((n - f + 1)!^2 * f!) where f = floor(n/2). - Peter Luschny, Sep 30 2018
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EXAMPLE
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Some solutions for n=5:
0 x 4 0 x 5 1 x 3 0 x 1 0 x 3 1 x 4 0 x 2
x 3 x x 1 x x 0 x x 4 x x 2 x x 0 x x 1 x
1 x 5 2 x 6 2 x 5 2 x 3 1 x 6 2 x 5 3 x 5
x 7 x x 3 x x 6 x x 6 x x 5 x x 6 x x 6 x
2 x 6 4 x 7 4 x 7 5 x 7 4 x 7 3 x 7 4 x 7
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MAPLE
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T := (n, k) -> (n-k+1)*(2*n-k)!/((n-k+1)!^2*k!):
a := n -> T(n, floor(n/2)): seq(a(n), n = 1..23); # Peter Luschny, Sep 30 2018
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MATHEMATICA
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Table[(n - Floor[n/2] + 1) (2 n - Floor[n/2])! / ((n -Floor[n/2] + 1)!^2 Floor[n/2]!), {n, 1, 30}] (* Vincenzo Librandi, Oct 01 2018 *)
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PROG
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(Magma) [(n-(n div 2)+1)*Factorial(2*n-(n div 2)) / (Factorial(n-(n div 2) +1)^2*Factorial((n div 2))): n in [1..30]]; // Vincenzo Librandi, Oct 01 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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