A301851 Table read by antidiagonals: T(n, k) gives the number of distinct distances on an n X k pegboard.

1, 2, 2, 3, 3, 3, 4, 5, 5, 4, 5, 7, 6, 7, 5, 6, 9, 9, 9, 9, 6, 7, 11, 12, 10, 12, 11, 7, 8, 13, 15, 14, 14, 15, 13, 8, 9, 15, 18, 17, 15, 17, 18, 15, 9, 10, 17, 21, 21, 19, 19, 21, 21, 17, 10, 11, 19, 24, 25, 24, 20, 24, 25, 24, 19, 11, 12, 21, 27, 29, 29, 26, 26, 29, 29, 27, 21, 12

Offset: 1

Author

Peter Kagey, Mar 27 2018

Keywords

• nonn
• tabl

Comments

Main diagonal is A047800.

Examples

			The 4 X 6 pegboard has 17 distinct distances: 0, 1, sqrt(2), 2, sqrt(5), sqrt(8), 3, sqrt(10), sqrt(13), 4, sqrt(17), sqrt(18), sqrt(20), 5, sqrt(26), sqrt(29), and sqrt(34).
+---+---+---+---+---+---+
| * |   |   |   | 16| 25|
+---+---+---+---+---+---+
| 1 | 2 |   |   | 17| 26|
+---+---+---+---+---+---+
| 4 | 5 | 8 |   | 20| 29|
+---+---+---+---+---+---+
| 9 | 10| 13| 18|   | 34|
+---+---+---+---+---+---+
(As depicted, the pegs are at the center of each face.)
Square array begins:
  n\k|    1    2    3    4    5    6    7    8
  ---+----------------------------------------
    1|    1    2    3    4    5    6    7    8
    2|    2    3    5    7    9   11   13   15
    3|    3    5    6    9   12   15   18   21
    4|    4    7    9   10   14   17   21   25
    5|    5    9   12   14   15   19   24   29
    6|    6   11   15   17   19   20   26   31
    7|    7   13   18   21   24   26   27   33
    8|    8   15   21   25   29   31   33   34
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001481, A047800, A225273, A301853.

Programs

Haskell

import Data.List (nub)
a301851 n k = length $ nub [i^2 + j^2 | i <- [0..n-1], j <- [0..k-1]]