A292172 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with six.

52, 166, 425, 1116, 3392, 10872, 38795, 102634, 260334, 651704, 1707641, 4477199, 12277412, 30970764, 75239813, 181934538, 440594545, 1063081418, 2625678546, 6286974074, 14803016600, 34534616815, 80129926919, 185059517397, 431845849360, 997735570874

Offset

6,1

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 = 6..2000

Example

a(6) = 52: 612345, 613245, 613425, 613452, 613524, 613542, 614235, 614253, 614325, 614352, 614532, 615234, 615243, 615324, 615342, 615432, 621345, 623145, 623415, 623451, 624135, 624153, 624315, 624351, 624531, 625134, 625143, 625314, 625341, 625431, 631245, 631425, 631452, 632145, 632415, 632451, 634215, 634251, 634521, 635214, 635241, 635421, 642135, 642315, 642351, 642513, 642531, 643215, 643251, 643521, 645321, 654321.

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, 6)-b(0, n, 5):
seq(a(n), n=6..50);

Crossrefs

Column k=6 of A291684.

Sequence in context: A297627 A049059 A345240 * A166390 A161478 A288919

Adjacent sequences: A292169 A292170 A292171 * A292173 A292174 A292175

Keyword

nonn

Author

Alois P. Heinz, Sep 10 2017

Status

approved