A344009 The Tchoukaillon array of order infinity read by downward antidiagonals.

1, 2, 3, 4, 5, 7, 6, 8, 9, 13, 10, 11, 14, 15, 19, 12, 16, 17, 21, 25, 27, 18, 20, 23, 26, 29, 31, 39, 22, 24, 28, 33, 37, 41, 43, 49, 30, 32, 35, 38, 44, 45, 51, 61, 63, 34, 36, 40, 47, 50, 55, 62, 65, 67, 79, 42, 46, 52, 53, 57, 64, 69, 73, 85, 87, 91, 48, 54, 56, 66, 68, 74, 75, 86, 89, 99, 103, 109

Offset

1,2

References

D. E. Knuth, Bipartite Matching, The Art of Computer Programming, Vol. 4, Pre-fascicle 14A, June 8, 2021, http://cs.stanford.edu/~knuth/fasc14a.ps.gz. See Sect. 7.5.1, Exercise 13.

Links

Don Knuth, Antidiagonals n = 1..32

D. E. Knuth, The first 32 antidiagonals

D. E. Knuth, Tchoukaillon numbers, YouTube video, 2022.

Example

The array begins:
   1   2   4   6  10  12  18  22  30  34 ...
   3   5   8  11  16  20  24  32  36  46 ...
   7   9  14  17  23  28  35  40  52  56 ...
  13  15  21  26  33  38  47  53  66  71 ...
  19  25  29  37  44  50  57  68  77  88 ...
  27  31  41  45  55  64  74  81  95 100 ...
  39  43  51  62  69  75  93  98 115 124 ...
  49  61  65  73  86  97 104 122 131 146 ...
  63  67  85  89 101 111 128 134 157 161 ...
  79  87  99 105 125 129 149 159 177 188 ...
  ...
The initial antidiagonals are:
  [1],
  [2, 3],
  [4, 5, 7],
  [6, 8, 9, 13],
  [10, 11, 14, 15, 19],
  [12, 16, 17, 21, 25, 27],
  [18, 20, 23, 26, 29, 31, 39],
  [22, 24, 28, 33, 37, 41, 43, 49],
  [30, 32, 35, 38, 44, 45, 51, 61, 63],
  [34, 36, 40, 47, 50, 55, 62, 65, 67, 79],
  [42, 46, 52, 53, 57, 64, 69, 73, 85, 87, 91],
  [48, 54, 56, 66, 68, 74, 75, 86, 89, 99, 103, 109],
  [58, 59, 70, 71, 77, 81, 93, 97, 101, 105, 121, 123, 133],
  [60, 72, 76, 83, 88, 95, 98, 104, 111, 125, 127, 135, 139, 147],
  ...

Crossrefs

Rows: A002491, A344010, A344011, ...

Columns: A000960, A100287, A344012, ...

Sequence in context: A267112 A269392 A166277 * A145342 A248918 A318936

Adjacent sequences: A344006 A344007 A344008 * A344010 A344011 A344012

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 09 2021, based on an email from Don Knuth, Jun 08 2021

Status

approved