A269780 Table read by antidiagonals where T(i,j) is the location of the pair (i,j) in A269501.

1, 2, 4, 5, 3, 9, 10, 8, 7, 16, 17, 15, 6, 14, 25, 26, 24, 13, 12, 23, 36, 37, 35, 22, 11, 21, 34, 49, 50, 48, 33, 20, 19, 32, 47, 64, 65, 63, 46, 31, 18, 30, 45, 62, 81, 82, 80, 61, 44, 29, 28, 43, 60, 79, 100, 101, 99, 78, 59, 42, 27, 41, 58, 77, 98, 121, 122, 120, 97, 76, 57, 40, 39, 56, 75, 96, 119, 144

Offset: 1

Author

Franklin T. Adams-Watters, Mar 04 2016

Keywords

• nonn
• tabl

Comments

This is trivially a permutation of the positive integers.

The "location" of the pair is taken to be the index of the second element of the pair.

Examples

			The table starts:
   1,  2,  5, 10, 17, 26
   4,  3,  8, 15, 24, 35
   9,  7,  6, 13, 22, 33
  16, 14, 12, 11, 20, 31
  25, 23, 21, 19, 18, 29
  36, 34, 32, 30, 28, 27
		

Crossrefs

Cf. A269501, A097292, A002522 (top row, left shifted).

If 1 is subtracted from each term we get A316323.

Formula

T(i,j) :=

if i=1, then (j-1)^2 + 1,

if i>j, then i^2 - 2j + 2,

and otherwise j^2 - 2i + 3.