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

10,1

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

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);

Crossrefs

Column k=10 of A291684.

Sequence in context: A203089 A187113 A023356 * A198484 A252200 A234773

Adjacent sequences: A292173 A292174 A292175 * A292177 A292178 A292179

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved