A288911 Number of permutations p of [n] such that 0p has a nonincreasing up-jump sequence.

1, 1, 2, 5, 19, 80, 416, 2306, 14588, 98053, 724183, 5633793, 47416901, 417050215, 3914152702, 38288228393, 395496623939, 4241350801439, 47715403637219, 555476398869869, 6744406721447538, 84548532634924758, 1100301545470162305, 14751287346427752887

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

Crossrefs

Cf. A288910, A288912, A291685.

Sequence in context: A222055 A228569 A204328 * A138911 A181513 A262165

Adjacent sequences: A288908 A288909 A288910 * A288912 A288913 A288914

Keyword

nonn

Author

Alois P. Heinz, Sep 01 2017

Status

approved