

A320600


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.


0




OFFSET

1,2


COMMENTS

a(n) is even, because if a permutation is minimal, then so is its reverse.
The minimal sum is given by A327672.  Peter Kagey, Sep 21 2019


LINKS

Table of n, a(n) for n=1..9.
Sung Soo Kim, Problems and Solutions, Mathematics Magazine, 91:4 (2018), 310.
Michael Reid, Problems and Solutions, Mathematics Magazine, 92:4 (2019), 314.


EXAMPLE

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.


CROSSREFS

Sequence in context: A092524 A137787 A225171 * A290606 A155952 A277445
Adjacent sequences: A320597 A320598 A320599 * A320601 A320602 A320603


KEYWORD

nonn,more


AUTHOR

Peter Kagey, Oct 16 2018


STATUS

approved



