A288912 Number of permutations p of [n] such that 0p has a nonincreasing down-jump sequence.

1, 1, 2, 6, 23, 106, 558, 3284, 21200, 148539, 1119273, 9013112, 77106652, 697811164, 6652604804, 66593158893, 697756930786, 7633155361594, 86969814549075, 1029939820075074, 12652809025029242, 160977119684852369, 2117642963178349336, 28763717105362639324

Offset

0,3

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 = 0..200

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, t), j=1..o))
    end:
a:= n-> b(0, n$2):
seq(a(n), n=0..30);

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,
     Sum[b[u - j, o + j - 1, j], {j, Min[t, u]}] +
     Sum[b[u + j - 1, o - j, t], {j, o}]];
a[n_] := b[0, n, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Aug 31 2021, after Alois P. Heinz *)

Crossrefs

Cf. A288910, A288911, A291685.

Sequence in context: A352367 A192315 A325297 * A193321 A263780 A363417

Adjacent sequences: A288909 A288910 A288911 * A288913 A288914 A288915

Keyword

nonn

Author

Alois P. Heinz, Sep 01 2017

Status

approved