5,1

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 = 5..3335

a(5) = 16: 51234, 51324, 51342, 51423, 51432, 52134, 52314, 52341, 52413, 52431, 53124, 53142, 53214, 53241, 53421, 54321.

a(6) = 47: 512346, 513246, 513426, 513462, 513624, ..., 543216, 543261, 543621, 546321, 564321.

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, 5)-b(0, n, 4):

seq(a(n), n=5..50);

Column k=5 of A291684.

Sequence in context: A204616 A204800 A194268 * A204609 A233063 A208634

Adjacent sequences: A292168 A292169 A292170 * A292172 A292173 A292174

Alois P. Heinz, Sep 10 2017

approved