

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
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OFFSET

3,1


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 = 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(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, 3)b(0, n, 2):
seq(a(n), n=3..50);


CROSSREFS

Column k=3 of A291684.
Sequence in context: A055192 A108555 A323397 * A283799 A225798 A303204
Adjacent sequences: A292166 A292167 A292168 * A292170 A292171 A292172


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Sep 10 2017


STATUS

approved



