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%I #16 Sep 24 2015 01:40:10
%S 0,1,1,2,0,2,3,3,4,3,4,2,0,5,4,5,5,5,1,2,5,6,4,1,4,5,3,6,7,7,3,0,0,4,
%T 7,7,8,6,8,2,3,1,12,6,8,9,9,10,9,1,2,13,13,10,9,10,8,6,11,10,0,18,12,
%U 14,11,10,11,11,11,7,8,11,19,19,16,15,8,11,12,10,7,10,11,9,0,18,20,17,16,9,12,13,13,9,6,6,10,1,1,22,21,14,17,18,13,14,12,14,8,9,7,14,0,2,23,22,15,6,19,14
%N Transpose of square array A261096.
%C Each row and column is a permutation of A001477. See the comments at A261096.
%H Antti Karttunen, <a href="/A261097/b261097.txt">Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cayley_table">Cayley table</a>
%F By conjugating with related permutations and arrays:
%F A(i,j) = A056019(A261096(A056019(i),A056019(j))).
%F A(i,j) = A060119(A261217(A060126(i),A060126(j))).
%F A(i,j) = A060120(A261216(A060127(i),A060127(j))).
%e The top left corner of the array:
%e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
%e 1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, ...
%e 2, 4, 0, 5, 1, 3, 8, 10, 6, 11, 7, 9, 14, ...
%e 3, 5, 1, 4, 0, 2, 9, 11, 7, 10, 6, 8, 15, ...
%e 4, 2, 5, 0, 3, 1, 10, 8, 11, 6, 9, 7, 16, ...
%e 5, 3, 4, 1, 2, 0, 11, 9, 10, 7, 8, 6, 17, ...
%e 6, 7, 12, 13, 18, 19, 0, 1, 14, 15, 20, 21, 2, ...
%e 7, 6, 13, 12, 19, 18, 1, 0, 15, 14, 21, 20, 3, ...
%e 8, 10, 14, 16, 20, 22, 2, 4, 12, 17, 18, 23, 0, ...
%e 9, 11, 15, 17, 21, 23, 3, 5, 13, 16, 19, 22, 1, ...
%e 10, 8, 16, 14, 22, 20, 4, 2, 17, 12, 23, 18, 5, ...
%e 11, 9, 17, 15, 23, 21, 5, 3, 16, 13, 22, 19, 4, ...
%e 12, 18, 6, 19, 7, 13, 14, 20, 0, 21, 1, 15, 8, ...
%e ...
%Y Transpose: A261096.
%Y Row 0 & Column 0: A001477 (identity permutation).
%Y Row 1: A004442.
%Y Column 1: A261098.
%Y Main diagonal: A261099.
%Y Cf. also A055089, A195663.
%Y Cf. also A261216, A261217 (similar arrays, but using different orderings of permutations).
%Y Permutations used in conjugation-formulas: A056019, A060119, A060120, A060126, A060127.
%K nonn,tabl
%O 0,4
%A _Antti Karttunen_, Aug 26 2015
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