OFFSET
7,1
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 = 7..2000
EXAMPLE
a(7) = 189: 7123456, 7132456, 7134256, 7134526, 7134562, 7135246, 7135264, 7135426, 7135462, 7135642, ..., 7534621, 7536214, 7536241, 7536421, 7543216, 7543261, 7543621, 7546321, 7564321, 7654321.
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, 7)-b(0, n, 6):
seq(a(n), n=7..50);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2017
STATUS
approved