

A338885


Irregular triangle read by rows in which the nth row lists all numbers k such that there exists a diagonal lattice rectangle touching all four sides of a n X k rectangle.


2



2, 3, 4, 5, 4, 5, 7, 6, 9, 10, 5, 7, 8, 11, 13, 7, 8, 10, 13, 16, 17, 6, 9, 11, 12, 15, 19, 21, 6, 8, 10, 11, 14, 17, 22, 25, 26, 7, 9, 10, 11, 13, 14, 16, 17, 19, 25, 29, 31, 9, 12, 13, 15, 18, 20, 21, 28, 33, 36, 37, 7, 8, 11, 12, 13, 14, 15, 17, 20, 22, 23
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OFFSET

2,1


COMMENTS

A diagonal lattice rectangle is a rectangle with integer coordinates and no side parallel to the xaxis.
Conjecture: The smallest number in the nth row is A228286(n).
Conjecture: The largest number in the nth row is A033638(n).


LINKS

Peter Kagey, Table of n, a(n) for n = 2..11808 (first 100 rows, flattened)
Code Golf Stack Exchange, Rectangles in rectangles


EXAMPLE

Table begins:
n  nth row
+
2  2
3  3
4  4, 5
5  4, 5, 7
6  6, 9, 10
7  5, 7, 8, 11, 13
8  7, 8, 10, 13, 16, 17
9  6, 9, 11, 12, 15, 19, 21
10  6, 8, 10, 11, 14, 17, 22, 25, 26
11  7, 9, 10, 11, 13, 14, 16, 17, 19, 25, 29, 31
12  9, 12, 13, 15, 18, 20, 21, 28, 33, 36, 37
For n = 6, three of the diagonal lattice rectangles that touch the yaxis, xaxis, and line x = 6 are:
(2 ,6), (0,2), (4,0), (6,4);
(2, 9), (0,8), (4,0), (6,1); and
(3,10), (0,9), (3,0), (6,1);
which have maximum yvalues of 6, 9, and 10 respectively.


CROSSREFS

Cf. A033638, A085582, A113751, A228286.
Cf. A338886 (row lengths).
Sequence in context: A284000 A309293 A244904 * A238288 A323161 A152739
Adjacent sequences: A338882 A338883 A338884 * A338886 A338887 A338888


KEYWORD

nonn,tabf


AUTHOR

Peter Kagey, Nov 14 2020


STATUS

approved



