A261097 Transpose of square array A261096.

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

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: A354438 A354470 A141692 * A335335 A261217 A352957

Adjacent sequences: A261094 A261095 A261096 * A261098 A261099 A261100

Keyword

nonn,tabl

Author

Antti Karttunen, Aug 26 2015

Status

approved