The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000707 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A000707

Number of permutations of [1,2,...,n] with n-1 inversions.
(history; published version)

#93 by Alois P. Heinz at Mon Jun 26 10:36:34 EDT 2023

STATUS

editing

approved

#92 by Alois P. Heinz at Mon Jun 26 10:36:31 EDT 2023

COMMENTS

For n>0: a(n) is the number of compositions of n-1 into n-1 nonnegative parts such that the i-th part i is not larger than i. a(4) = 6: [0,0,3], [0,1,2], [0,2,1], [1,0,2], [1,1,1], [1,2,0]. - Alois P. Heinz, Jun 26 2023

STATUS

approved

editing

#91 by Alois P. Heinz at Mon Jun 26 10:35:45 EDT 2023

STATUS

editing

approved

#90 by Alois P. Heinz at Mon Jun 26 10:35:41 EDT 2023

COMMENTS

For n>0: a(n) is the number of compositions of n-1 into n-1 nonnegative parts such that part i is not larger than i. a(4) = 6: [0,0,3], [0,1,2], [0,2,1], [1,0,2], [1,1,1], [1,2,0]. - Alois P. Heinz, Jun 26 2023

#89 by Alois P. Heinz at Mon Jun 26 10:29:34 EDT 2023

MAPLE

b:= proc(n, i) option remember; `if`(n>i*(i+1)/2, 0,

`if`(n=0, 1, add(b(n-j, i-1), j=0..min(n, i))))

end:

a:= n-> b(n-1$2):

seq(a(n), n=1..27); # Alois P. Heinz, Jun 26 2023

STATUS

approved

editing

#88 by OEIS Server at Mon Jun 26 10:25:39 EDT 2023

LINKS

Alois P. Heinz, <a href="/A000707/b000707_1.txt">Table of n, a(n) for n = 1..1665</a>

#87 by Alois P. Heinz at Mon Jun 26 10:25:39 EDT 2023

STATUS

editing

approved

Discussion

Mon Jun 26

10:25

OEIS Server: Installed new b-file as b000707.txt.  Old b-file is now b000707_1.txt.

#86 by Alois P. Heinz at Mon Jun 26 10:25:35 EDT 2023

LINKS

Alois P. Heinz, <a href="/A000707/b000707_1.txt">Table of n, a(n) for n = 1..10001665</a>

STATUS

approved

editing

#85 by Joerg Arndt at Mon Aug 29 02:21:45 EDT 2022

STATUS

reviewed

approved

#84 by Michel Marcus at Mon Aug 29 01:05:13 EDT 2022

STATUS

proposed

reviewed