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A292175 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with nine. 2
2621, 9459, 26167, 69404, 188735, 558151, 1745634, 5935728, 20786804, 77416352, 219059475, 578513498, 1500419043, 3908857765, 10470345790, 28385741484, 79729201108, 221303407539, 630847591899, 1653827513009, 4173815556603, 10415200154855, 25901062216475 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 26 05:42 EDT 2019. Contains 326329 sequences. (Running on oeis4.)