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A292173 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 25 13:59 EDT 2021. Contains 348253 sequences. (Running on oeis4.)