A292171 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with five.

16, 47, 117, 327, 988, 3392, 8739, 21372, 53596, 135791, 362528, 887060, 2117839, 4997836, 11731828, 28229247, 66196942, 152418888, 347010327, 784580873, 1794241712, 4064606075, 9109879761, 20253187230, 44774963928, 99368298849, 219638865759, 482519177252

Offset

5,1

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 = 5..3335

Example

a(5) = 16: 51234, 51324, 51342, 51423, 51432, 52134, 52314, 52341, 52413, 52431, 53124, 53142, 53214, 53241, 53421, 54321.
a(6) = 47: 512346, 513246, 513426, 513462, 513624, ..., 543216, 543261, 543621, 546321, 564321.

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, 5)-b(0, n, 4):
seq(a(n), n=5..50);

Crossrefs

Column k=5 of A291684.

Sequence in context: A204616 A204800 A194268 * A204609 A233063 A208634

Adjacent sequences: A292168 A292169 A292170 * A292172 A292173 A292174

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved