A292169 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with three.

2, 5, 12, 36, 81, 174, 413, 889, 1870, 4031, 8490, 17580, 36647, 75801, 154676, 316873, 646614, 1309277, 2653548, 5358828, 10786403, 21697201, 43539382, 87208388, 174392929, 348359875, 694913277, 1384281163, 2755398784, 5476741024, 10878139055, 21590446589

Offset

3,1

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 = 3..3424

Example

a(3) = 2: 312, 321.
a(4) = 5: 3124, 3142, 3214, 3241, 3421
a(5) = 12: 31245, 31425, 31452, 32145, 32415, 32451, 34215, 34251, 34521, 35214, 35241, 35421.

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, 3)-b(0, n, 2):
seq(a(n), n=3..50);

Crossrefs

Column k=3 of A291684.

Sequence in context: A055192 A108555 A323397 * A283799 A225798 A303204

Adjacent sequences: A292166 A292167 A292168 * A292170 A292171 A292172

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved