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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

Antti Karttunen, Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array

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: A185815 A003987 A141692 * A261217 A245230 A284268

Adjacent sequences:  A261094 A261095 A261096 * A261098 A261099 A261100

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Aug 26 2015

STATUS

approved

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Last modified February 20 02:47 EST 2018. Contains 299357 sequences. (Running on oeis4.)