A292175 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with nine.

2621, 9459, 26167, 69404, 188735, 558151, 1745634, 5935728, 20786804, 77416352, 219059475, 578513498, 1500419043, 3908857765, 10470345790, 28385741484, 79729201108, 221303407539, 630847591899, 1653827513009, 4173815556603, 10415200154855, 25901062216475

Offset

9,1

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 = 9..2000

Example

a(9) = 2621: 912345678, 913245678, 913425678, 913452678, 913456278, 913456728, 913456782, 913524678, 913526478, 913526748, ..., 975846321, 975864321, 976543218, 976543281, 976543821, 976548321, 976584321, 976854321, 978654321, 987654321.

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, 9)-b(0, n, 8):
seq(a(n), n=9..50);

Crossrefs

Column k=9 of A291684.

Sequence in context: A238921 A156398 A139675 * A295482 A236621 A221941

Adjacent sequences: A292172 A292173 A292174 * A292176 A292177 A292178

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved