2,2

An up-jump j occurs at position i in p if p_{i} > p_{i-1} and j is the index of p_i in the increasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are larger than p_{i-1}. A down-jump j occurs at position i in p if p_{i} < p_{i-1} and j is the index of p_i in the decreasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are smaller than p_{i-1}. First index in the lists is 1 here.

Alois P. Heinz, Table of n, a(n) for n = 2..3630

a(2) = 1: 21.

a(3) = 2: 213, 231.

a(4) = 5: 2134, 2314, 2341, 2413, 2431.

a(5) = 9: 21345, 23145, 23415, 23451, 24135, 24153, 24315, 24351, 24531.

a(6) = 17: 213456, 231456, 234156, 234516, 234561, 241356, 241536, 241563, 243156, 243516, 243561, 245316, 245361, 245631, 246315, 246351, 246531.

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,

add(b(u-j, o+j-1, j), j=1..min(t, u))+

add(b(u+j-1, o-j, j), j=1..min(t, o)))

end:

a:= n-> b(0, n, 2)-b(0, n, 1):

seq(a(n), n=2..50);

Column k=2 of A291684.

Sequence in context: A082281 A285458 A000569 * A322304 A394989 A182992

Adjacent sequences: A292165 A292166 A292167 * A292169 A292170 A292171

Alois P. Heinz, Sep 10 2017

approved