The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A288912

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A288912

Number of permutations p of [n] such that 0p has a nonincreasing down-jump sequence.
(history; published version)

#12 by Alois P. Heinz at Tue Aug 31 07:41:45 EDT 2021

STATUS

proposed

approved

#11 by Jean-François Alcover at Tue Aug 31 07:26:30 EDT 2021

STATUS

editing

proposed

#10 by Jean-François Alcover at Tue Aug 31 07:26:25 EDT 2021

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,

Sum[b[u - j, o + j - 1, j], {j, Min[t, u]}] +

Sum[b[u + j - 1, o - j, t], {j, o}]];

a[n_] := b[0, n, n];

Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Aug 31 2021, after Alois P. Heinz *)

STATUS

approved

editing

#9 by Alois P. Heinz at Fri Sep 01 22:00:57 EDT 2017

STATUS

editing

approved

#8 by Alois P. Heinz at Fri Sep 01 22:00:53 EDT 2017

LINKS

Alois P. Heinz, <a href="/A288912/b288912.txt">Table of n, a(n) for n = 0..200</a>

#7 by Alois P. Heinz at Fri Sep 01 17:46:51 EDT 2017

NAME

0

Number of permutations p of [n] such that 0p has a nonincreasing down-jump sequence.

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.

#6 by Alois P. Heinz at Fri Sep 01 17:44:05 EDT 2017

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, t), j=1..o))

end:

a:= n-> b(0, n$2):

seq(a(n), n=0..30);

CROSSREFS

Cf. A288910, A288911, A291685.

#5 by Alois P. Heinz at Fri Sep 01 17:34:05 EDT 2017

NAME

allocated for Alois P. Heinz

0

DATA

1, 1, 2, 6, 23, 106, 558, 3284, 21200, 148539, 1119273, 9013112, 77106652, 697811164, 6652604804, 66593158893, 697756930786, 7633155361594, 86969814549075, 1029939820075074, 12652809025029242, 160977119684852369, 2117642963178349336, 28763717105362639324

OFFSET

0,3

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Sep 01 2017

STATUS

approved

editing

#4 by Alois P. Heinz at Fri Sep 01 17:34:05 EDT 2017

NAME

allocated for Alois P. Heinz

KEYWORD

recycled

allocated

#3 by R. J. Mathar at Thu Aug 31 12:57:43 EDT 2017

STATUS

editing

approved