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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2017
STATUS
approved