A292174 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with eight.

683, 2400, 6471, 16817, 47123, 141118, 469662, 1609176, 5935728, 16491722, 43160750, 110362553, 289385731, 767677544, 2119594253, 5810801164, 16404580983, 42548928025, 106693231930, 263735820713, 650860901400, 1621682678763, 4064296654515, 10129808852568

Offset

8,1

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 = 8..2000

Example

a(8) = 683: 81234567, 81324567, 81342567, 81345267, 81345627, 81345672, 81352467, 81352647, 81352674, 81354267, ..., 86473251, 86473521, 86475321, 86543217, 86543271, 86543721, 86547321, 86574321, 86754321, 87654321.

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, 8)-b(0, n, 7):
seq(a(n), n=8..50);

Crossrefs

Column k=8 of A291684.

Sequence in context: A300193 A234502 A089201 * A065123 A269486 A239272

Adjacent sequences: A292171 A292172 A292173 * A292175 A292176 A292177

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved