A338885 - OEIS

A338885

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

A diagonal lattice rectangle is a rectangle with integer coordinates and no side parallel to the x-axis.

Conjecture: The smallest number in the n-th row is A228286(n).

Conjecture: The largest number in the n-th 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 | n-th 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 y-axis, x-axis, 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 y-values of 6, 9, and 10 respectively.

CROSSREFS

Cf. A033638, A085582, A113751, A228286.

Cf. A338886 (row lengths).

Sequence in context: A284000 A309293 A244904 * A238288 A376074 A323161

Adjacent sequences: A338882 A338883 A338884 * A338886 A338887 A338888

KEYWORD

nonn,tabf

AUTHOR

Peter Kagey, Nov 14 2020

STATUS

approved