A195663 Array read by antidiagonals: Consecutive finite permutations of positive integers in reverse colexicographic order.

1, 2, 2, 3, 1, 1, 4, 3, 3, 3, 5, 4, 2, 1, 2, 6, 5, 4, 2, 3, 3, 7, 6, 5, 4, 1, 2, 1, 8, 7, 6, 5, 4, 1, 2, 2, 9, 8, 7, 6, 5, 4, 4, 1, 1, 10, 9, 8, 7, 6, 5, 3, 4, 4, 4, 11, 10, 9, 8, 7, 6, 5, 3, 2, 1, 2, 12, 11, 10, 9, 8, 7, 6, 5, 3, 2, 4, 4, 13, 12, 11, 10, 9, 8, 7, 6, 5, 3, 1, 2, 1, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 3, 1, 3, 3

Offset

0,2

Comments

Row n is the n-th finite permutation of {1,2,3,4,...}.

Links

Tilman Piesk, Table of n, a(n) for n = 0..7259

Tilman Piesk, Detailed table of the 24 permutations of 1...4

Tilman Piesk, Table of the 40320  permutations of 1...8, a supporting file of A198380

OEIS-Wiki, Orderings section rev colex

Tilman Piesk, MATLAB code used for the calculation

Formula

a(n) = A195664(n)+1.

Example

The first 24 permutations of positive integers in rev colex order:
00  -->  1 2 3 4 5 6 7 8 ...
01  -->  2 1 3 4 ...
02  -->  1 3 2 4 ...
03  -->  3 1 2 4 ...
04  -->  2 3 1 4 ...
05  -->  3 2 1 4 ...
06  -->  1 2 4 3 ...
07  -->  2 1 4 3 ...
08  -->  1 4 2 3 ...
09  -->  4 1 2 3 ...
10  -->  2 4 1 3 ...
11  -->  4 2 1 3 ...
12  -->  1 3 4 2 ...
13  -->  3 1 4 2 ...
14  -->  1 4 3 2 ...
15  -->  4 1 3 2 ...
16  -->  3 4 1 2 ...
17  -->  4 3 1 2 ...
18  -->  2 3 4 1 ...
19  -->  3 2 4 1 ...
20  -->  2 4 3 1 ...
21  -->  4 2 3 1 ...
22  -->  3 4 2 1 ...
23  -->  4 3 2 1 ...

Crossrefs

Cf. A055089 (a very compact representation of these permutations).

Cf. A195664 (same for nonnegative integers, so all entries are smaller by 1).

Sequence in context: A328732 A130795 A367634 * A362749 A264010 A071435

Adjacent sequences: A195660 A195661 A195662 * A195664 A195665 A195666

Keyword

nonn,tabl

Author

Tilman Piesk, Sep 22 2011

Status

approved