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A320600
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Let w = (w_1, w_2, ..., w_n) be a permutation of the integers {1, 2, ..., n}, and let f(k, w) be the length of the longest monotone subsequence of (w_k, w_{k+1}, ..., w_n) starting with w_k. Then a(n) is the number of permutations w in S_n such that Sum_{k=1..n} f(k,w) is minimized.
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0
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OFFSET
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1,2
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COMMENTS
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a(n) is even, because if a permutation is minimal, then so is its reverse.
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LINKS
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EXAMPLE
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For n = 4 the a(4) = 4 permutations are
w_1 = (2,1,4,3),
w_2 = (2,4,1,3),
w_3 = (3,1,4,2), and
w_4 = (3,4,1,2).
In each case, f(1,w_i) + f(2,w_i) + f(3,w_i) + f(4,w_i) = A327672(4) = 7.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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