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Array read by antidiagonals: Consecutive finite permutations of positive integers in reverse colexicographic order.
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%I #51 Feb 17 2019 05:36:41

%S 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,

%T 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,

%U 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

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

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

%H Tilman Piesk, <a href="/A195663/b195663.txt">Table of n, a(n) for n = 0..7259</a>

%H Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutation_list_with_matrices.svg">Detailed table of the 24 permutations of 1...4</a>

%H Tilman Piesk, <a href="/A198380/a198380_1.txt">Table of the 40320 permutations of 1...8</a>, a supporting file of A198380

%H OEIS-Wiki, <a href="http://oeis.org/wiki/Orderings">Orderings</a> section <a href="http://oeis.org/wiki/Orderings#Reverse_colexicographic_order">rev colex</a>

%H Tilman Piesk, <a href="/A195663/a195663.txt">MATLAB code</a> used for the calculation

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

%e The first 24 permutations of positive integers in rev colex order:

%e 00 --> 1 2 3 4 5 6 7 8 ...

%e 01 --> 2 1 3 4 ...

%e 02 --> 1 3 2 4 ...

%e 03 --> 3 1 2 4 ...

%e 04 --> 2 3 1 4 ...

%e 05 --> 3 2 1 4 ...

%e 06 --> 1 2 4 3 ...

%e 07 --> 2 1 4 3 ...

%e 08 --> 1 4 2 3 ...

%e 09 --> 4 1 2 3 ...

%e 10 --> 2 4 1 3 ...

%e 11 --> 4 2 1 3 ...

%e 12 --> 1 3 4 2 ...

%e 13 --> 3 1 4 2 ...

%e 14 --> 1 4 3 2 ...

%e 15 --> 4 1 3 2 ...

%e 16 --> 3 4 1 2 ...

%e 17 --> 4 3 1 2 ...

%e 18 --> 2 3 4 1 ...

%e 19 --> 3 2 4 1 ...

%e 20 --> 2 4 3 1 ...

%e 21 --> 4 2 3 1 ...

%e 22 --> 3 4 2 1 ...

%e 23 --> 4 3 2 1 ...

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

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

%K nonn,tabl

%O 0,2

%A _Tilman Piesk_, Sep 22 2011