A083362 Square table, read by antidiagonals, of least distinct positive integers such that the sum of any two consecutive terms in any row is a square number.

1, 3, 2, 6, 7, 4, 10, 9, 5, 8, 15, 16, 11, 17, 12, 21, 20, 14, 19, 13, 18, 28, 29, 22, 30, 23, 31, 24, 36, 35, 27, 34, 26, 33, 25, 32, 45, 46, 37, 47, 38, 48, 39, 49, 40, 55, 54, 44, 53, 43, 52, 42, 51, 41, 50, 66, 67, 56, 68, 57, 69, 58, 70, 59, 71, 60, 78, 77, 65, 76, 64, 75

Offset

0,2

Comments

A permutation of the natural numbers.

Links

Table of n, a(n) for n=0..71.

Formula

T(0, k) = (k+1)*(k+2)/2 for k>=0, T(n, 0) = floor((n+1)^2/2) for n>0, T(n, k+1) = (2*floor((n+1)/2) + k+1)^2 - T(n, k) for n>0 and k>=0.

Example

Table begins:
   1   3   6  10  15  21  28  36  45  55  66 ...
   2   7   9  16  20  29  35  46  54  67  77 ...
   4   5  11  14  22  27  37  44  56  65  79 ...
   8  17  19  30  34  47  53  68  76  93 103 ...
  12  13  23  26  38  43  57  64  80  89 107 ...
  18  31  33  48  52  69  75  94 102 123 133 ...
  24  25  39  42  58  63  81  88 108 117 139 ...
  32  49  51  70  74  95 101 124 132 157 167 ...
  40  41  59  62  82  87 109 116 140 149 175 ...
  50  71  73  96 100 125 131 158 166 195 205 ...
  60  61  83  86 110 115 141 148 176 185 215 ...
  72  97  99 126 130 159 165 196 204 237 247 ...

Crossrefs

Cf. A083363 (diagonal), A083364 (antidiagonal sums).

Cf. A000217 (1st row), A080476 (1st column).

Sequence in context: A268826 A182849 A120231 * A182847 A182869 A335409

Adjacent sequences: A083359 A083360 A083361 * A083363 A083364 A083365

Keyword

nonn,tabl,nice

Author

Paul D. Hanna, Apr 27 2003

Status

approved