PROG
(MAGMAMagma) [(n/2)*Binomial(n-1, Floor((n-1)/2)) - 2^(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 01 2013
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(MAGMAMagma) [(n/2)*Binomial(n-1, Floor((n-1)/2)) - 2^(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 01 2013
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a(2n2*n) = 2*A000531(n-1); a(2n2*n+1) = A000531(n). - Max Alekseyev, Sep 30 2013
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total Total number of descents in all faro permutations of length n-1. Faro permutations are permutations avoiding the three consecutive patterns 231, 321 and 312. They are obtained by a perfect faro shuffle of two nondecreasing words of lengths differing by at most one. See also A340567, A340568 and A340569. - Sergey Kirgizov, Jan 11 2021
Popularity (total number) of descents (consecutive patterns 21) in all faro permutations of length n-1. Faro permutations are permutations avoiding the three consecutive patterns 231, 321 and 312. They are obtained by a perfect faro shuffle of two nondecreasing words of lengths differing by at most one. See also A340567, A340568 and A340569. - Sergey Kirgizov, Jan 11 2021
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Popularity (total number) of descents (consecutive patterns 21) in all faro permutations of length n-1. Faro permutations are permutations avoiding the three consecutive patterns 231, 321 and 312. They are obtained by a perfect faro shuffle of two nondecreasing words of lengths differing by at most one. See also A340567, A340568 and A340569 . - Sergey Kirgizov, Jan 11 2021
Popularity (total number) of descents (consecutive patterns 21) in all faro permutations of length n-1. Faro permutations are permutations avoiding the three consecutive patterns 231, 321 and 312. They are obtained by a perfect faro shuffle of two nondecreasing words of lengths differing by at most one. See also A340567, A340568 and A340569 - Sergey Kirgizov, Jan 11 2021