Source code in the jq programming language

def odd_magic_square:
  if type != "number" or . % 2 == 0 or . <= 0
  then error("odd_magic_square requires an odd positive integer")
  else
    . as $n
    | reduce range(1; 1 + ($n*$n)) as $i
         ( [0, (($n-1)/2), []];
 	  .[0] as $x | .[1] as $y
          | .[2]
	  | setpath([$x, $y]; $i )
          | if getpath([(($x+$n-1) % $n), (($y+$n+1) % $n)])
            then [(($x+$n+1) % $n), $y, .]
            else [ (($x+$n-1) % $n), (($y+$n+1) % $n), .]
 	    end )  | .[2]
  end ;

def task:
  def pp: if length == 0 then empty
          else "\(.[0])", (.[1:] | pp )
          end;
  "The magic sum for a square of size \(.) is \( (.*. + 1)*./2 ):",
    (odd_magic_square | pp)
;

(3, 5, 9) | task

$ jq -n -r -M -c -f odd_magic_square.jq
The magic sum for a square of size 3 is 15:
[8,1,6]
[3,5,7]
[4,9,2]
The magic sum for a square of size 5 is 65:
[17,24,1,8,15]
[23,5,7,14,16]
[4,6,13,20,22]
[10,12,19,21,3]
[11,18,25,2,9]
The magic sum for a square of size 9 is 369:
[47,58,69,80,1,12,23,34,45]
[57,68,79,9,11,22,33,44,46]
[67,78,8,10,21,32,43,54,56]
[77,7,18,20,31,42,53,55,66]
[6,17,19,30,41,52,63,65,76]
[16,27,29,40,51,62,64,75,5]
[26,28,39,50,61,72,74,4,15]
[36,38,49,60,71,73,3,14,25]
[37,48,59,70,81,2,13,24,35]