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Table read by antidiagonals where T(i,j) is the location of the pair (i,j) in A269501.
3

%I #20 Jul 04 2018 10:35:55

%S 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,

%T 34,49,50,48,33,20,19,32,47,64,65,63,46,31,18,30,45,62,81,82,80,61,44,

%U 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

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

%C This is trivially a permutation of the positive integers.

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

%F T(i,j) :=

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

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

%F and otherwise j^2 - 2i + 3.

%e The table starts:

%e 1, 2, 5, 10, 17, 26

%e 4, 3, 8, 15, 24, 35

%e 9, 7, 6, 13, 22, 33

%e 16, 14, 12, 11, 20, 31

%e 25, 23, 21, 19, 18, 29

%e 36, 34, 32, 30, 28, 27

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

%Y If 1 is subtracted from each term we get A316323.

%K nonn,tabl

%O 1,2

%A _Franklin T. Adams-Watters_, Mar 04 2016