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A292174 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with eight. 2
683, 2400, 6471, 16817, 47123, 141118, 469662, 1609176, 5935728, 16491722, 43160750, 110362553, 289385731, 767677544, 2119594253, 5810801164, 16404580983, 42548928025, 106693231930, 263735820713, 650860901400, 1621682678763, 4064296654515, 10129808852568 (list; graph; refs; listen; history; text; internal format)
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

Column k=8 of A291684.

Sequence in context: A300193 A234502 A089201 * A065123 A269486 A239272

Adjacent sequences:  A292171 A292172 A292173 * A292175 A292176 A292177

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 10 2017

STATUS

approved

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Last modified August 25 21:00 EDT 2019. Contains 326324 sequences. (Running on oeis4.)