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A261097 Transpose of square array A261096. 6
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Each row and column is a permutation of A001477. See the comments at A261096.
LINKS
Wikipedia, Cayley table
FORMULA
By conjugating with related permutations and arrays:
A(i,j) = A056019(A261096(A056019(i),A056019(j))).
A(i,j) = A060119(A261217(A060126(i),A060126(j))).
A(i,j) = A060120(A261216(A060127(i),A060127(j))).
EXAMPLE
The top left corner of the array:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, ...
2, 4, 0, 5, 1, 3, 8, 10, 6, 11, 7, 9, 14, ...
3, 5, 1, 4, 0, 2, 9, 11, 7, 10, 6, 8, 15, ...
4, 2, 5, 0, 3, 1, 10, 8, 11, 6, 9, 7, 16, ...
5, 3, 4, 1, 2, 0, 11, 9, 10, 7, 8, 6, 17, ...
6, 7, 12, 13, 18, 19, 0, 1, 14, 15, 20, 21, 2, ...
7, 6, 13, 12, 19, 18, 1, 0, 15, 14, 21, 20, 3, ...
8, 10, 14, 16, 20, 22, 2, 4, 12, 17, 18, 23, 0, ...
9, 11, 15, 17, 21, 23, 3, 5, 13, 16, 19, 22, 1, ...
10, 8, 16, 14, 22, 20, 4, 2, 17, 12, 23, 18, 5, ...
11, 9, 17, 15, 23, 21, 5, 3, 16, 13, 22, 19, 4, ...
12, 18, 6, 19, 7, 13, 14, 20, 0, 21, 1, 15, 8, ...
...
CROSSREFS
Transpose: A261096.
Row 0 & Column 0: A001477 (identity permutation).
Row 1: A004442.
Column 1: A261098.
Main diagonal: A261099.
Cf. also A055089, A195663.
Cf. also A261216, A261217 (similar arrays, but using different orderings of permutations).
Permutations used in conjugation-formulas: A056019, A060119, A060120, A060126, A060127.
Sequence in context: A354438 A354470 A141692 * A335335 A261217 A352957
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Aug 26 2015
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)