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A107373
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a(n) = (n/2)*binomial(n-1, floor((n-1)/2)) - 2^(n-2).
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7
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0, 0, 1, 2, 7, 14, 38, 76, 187, 374, 874, 1748, 3958, 7916, 17548, 35096, 76627, 153254, 330818, 661636, 1415650, 2831300, 6015316, 12030632, 25413342, 50826684, 106853668, 213707336, 447472972, 894945944, 1867450648, 3734901296, 7770342787, 15540685574
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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FORMULA
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(1-n)*a(n) + 2*(n-1)*a(n-1) + 4*(n-2)*a(n-2) + 8*(-n+2)*a(n-3) = 0. - R. J. Mathar, May 26 2013
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MAPLE
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A133265 := n -> (n+2+(n-2)*(-1)^n)/2:
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MATHEMATICA
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Table[(n/2) Binomial[n-1, Floor[(n-1)/2]] - 2^(n-2), {n, 1, 40}] (* Vincenzo Librandi, Oct 01 2013 *)
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PROG
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(Magma) [(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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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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