A292168 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with two.

1, 2, 5, 9, 17, 31, 57, 101, 185, 333, 599, 1089, 1975, 3563, 6505, 11829, 21455, 39257, 71641, 130403, 239193, 437677, 799127, 1468777, 2693853, 4930871, 9079127, 16684737, 30605159, 56441227, 103900161, 190934999, 352606721, 650072239, 1196527319, 2212404279

Offset: 2

Author

Alois P. Heinz, Sep 10 2017

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Column k=2 of A291684.

Programs

Maple

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);