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

2,2

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.

Links

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

Example

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.

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);

Crossrefs

Column k=2 of A291684.

Sequence in context: A082281 A285458 A000569 * A322304 A182992 A115851

Adjacent sequences: A292165 A292166 A292167 * A292169 A292170 A292171

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved