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A292169 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with three. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A000105 A055192 A108555 * A283799 A225798 A032203

Adjacent sequences:  A292166 A292167 A292168 * A292170 A292171 A292172

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 10 2017

STATUS

approved

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Last modified February 23 18:54 EST 2018. Contains 299586 sequences. (Running on oeis4.)