

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
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OFFSET

1,2


COMMENTS



LINKS



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..n1], j < [0..k1]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



