A292173 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven.

189, 627, 1633, 4291, 12146, 38795, 129520, 469662, 1281977, 3286121, 8402785, 21706131, 58633404, 157849186, 439490771, 1128233084, 2793077829, 6823503775, 16758669067, 41349963758, 101704832977, 255372664080, 622178277449, 1484157011512, 3512057801972

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

Column k=7 of A291684.

Sequence in context: A348544 A211815 A347390 * A231394 A347383 A297229

Adjacent sequences: A292170 A292171 A292172 * A292174 A292175 A292176

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved