A292176 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with ten.

10061, 37702, 107175, 285492, 786489, 2249024, 6929078, 22322520, 77416352, 274792342, 1035050705, 2962838350, 7926847142, 20648853479, 54254560137, 143941539439, 393399319076, 1083862520072, 3084318416024, 8650938117110, 24829005575685, 65609605382112

Offset: 10

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..2000

Crossrefs

Column k=10 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, 10)-b(0, n, 9):
seq(a(n), n=10..50);