A388295 a(n) is the least possible difference between the areas of the largest and smallest rectangles in a 4 element set of distinct integer sided rectangles filling an n X n square.

4, 6, 6, 7, 10, 6, 10, 14, 8, 16, 13, 10, 22, 12, 18, 24, 14, 26, 22, 18, 32, 20, 26, 34, 20, 36, 30, 22, 42, 22, 31, 44, 24, 46, 35, 26, 54, 29, 42, 54, 31, 56, 46, 37, 64, 39, 50, 64, 37, 66, 54, 39, 74, 38, 53, 74, 40, 76, 57, 42, 86, 46, 66, 84, 48, 86, 70

Offset

4,1

Comments

Let the difference between the largest and smallest areas of the rectangles be called the defect. Then a(n) is the minimum defect.

Links

Table of n, a(n) for n=4..70.

Example

For n = 4, there are three sets of rectangles:
  {(1 X 1), (1 X 3), (1 X 4), (2 X 4)} with defect = 8 - 1 = 7,
  {(1 X 1), (1 X 2), (1 X 4), (3 X 3)} with defect = 9 - 1 = 8,
  {(1 X 2), (1 X 4), (2 X 2), (2 X 3)} with defect = 6 - 2 = 4.
Therefore, a(4) = 4 since this is the minimum defect.

Crossrefs

Cf. A387171, A385153 (3-dimensional version).

Sequence in context: A103413 A103412 A103411 * A200118 A254275 A074672

Adjacent sequences: A388292 A388293 A388294 * A388296 A388297 A388298

Keyword

nonn

Author

Janaka Rodrigo, Sep 16 2025

Extensions

More terms from Sean A. Irvine, Oct 27 2025

Status

approved