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A301851 Table read by antidiagonals: T(n, k) gives the number of distinct distances on an n X k pegboard. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Main diagonal is A047800.

LINKS

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

EXAMPLE

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

PROG

(Haskell)

import Data.List (nub)

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

CROSSREFS

Cf. A001481, A047800, A225273, A301853.

Sequence in context: A350066 A135646 A334922 * A101646 A166079 A269381

Adjacent sequences:  A301848 A301849 A301850 * A301852 A301853 A301854

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Mar 27 2018

STATUS

approved

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Last modified June 26 13:14 EDT 2022. Contains 354883 sequences. (Running on oeis4.)