

A292168


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


2



1, 2, 5, 9, 17, 31, 57, 101, 185, 333, 599, 1089, 1975, 3563, 6505, 11829, 21455, 39257, 71641, 130403, 239193, 437677, 799127, 1468777, 2693853, 4930871, 9079127, 16684737, 30605159, 56441227, 103900161, 190934999, 352606721, 650072239, 1196527319, 2212404279
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OFFSET

2,2


COMMENTS

An upjump j occurs at position i in p if p_{i} > p_{i1} 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_{i1}. A downjump j occurs at position i in p if p_{i} < p_{i1} 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_{i1}. First index in the lists is 1 here.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..3630


EXAMPLE

a(2) = 1: 21.
a(3) = 2: 213, 231.
a(4) = 5: 2134, 2314, 2341, 2413, 2431.
a(5) = 9: 21345, 23145, 23415, 23451, 24135, 24153, 24315, 24351, 24531.
a(6) = 17: 213456, 231456, 234156, 234516, 234561, 241356, 241536, 241563, 243156, 243516, 243561, 245316, 245361, 245631, 246315, 246351, 246531.


MAPLE

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(uj, o+j1, j), j=1..min(t, u))+
add(b(u+j1, oj, j), j=1..min(t, o)))
end:
a:= n> b(0, n, 2)b(0, n, 1):
seq(a(n), n=2..50);


CROSSREFS

Column k=2 of A291684.
Sequence in context: A082281 A285458 A000569 * A322304 A182992 A115851
Adjacent sequences: A292165 A292166 A292167 * A292169 A292170 A292171


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Sep 10 2017


STATUS

approved



