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 A215287 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also Schröder paths of length n having floor(n/2) peaks. - Peter Luschny, Sep 30 2018 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA f3 = floor((n+1)/2); f4 = floor(n/2); a(n) = A060854(2,f3)*A060854(1,f4)*binomial(2*f3+1*f4,2*f3). a(n) = (n - f + 1)*(2*n - f)! / ((n - f + 1)!^2 * f!) where f = floor(n/2). - Peter Luschny, Sep 30 2018 EXAMPLE 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 MAPLE 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Column 3 of A215292. Cf. A060854, A060693. Sequence in context: A136846 A004663 A136853 * A316764 A331780 A290061 Adjacent sequences: A215284 A215285 A215286 * A215288 A215289 A215290 KEYWORD nonn AUTHOR R. H. Hardin, Aug 07 2012 STATUS approved

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Last modified February 1 10:32 EST 2023. Contains 359993 sequences. (Running on oeis4.)