A384724 a(n) is the number of 4 element sets of distinct integer sided strict rectangles that fill an n X n square.

0, 0, 0, 0, 5, 15, 39, 70, 132, 197, 311, 421, 606, 771, 1047, 1275, 1655, 1968, 2466, 2863, 3510, 4004, 4802, 5416, 6384, 7116, 8286, 9144, 10517, 11535, 13125, 14290, 16140, 17465, 19565, 21085, 23454, 25155, 27837, 29727, 32711, 34836, 38136, 40471, 44142, 46700, 50720, 53548, 57936, 61008

Offset

1,5

Comments

A strict rectangle is a rectangle that is not a square.

Links

Table of n, a(n) for n=1..50.

Example

a(5) = 5 sets of integer sided strict rectangles are:
  {(1 X 2), (1 X 3), (1 X 5), (3 X 5)},
  {(1 X 2), (1 X 3), (2 X 4), (3 X 4)},
  {(1 X 2), (1 X 5), (2 X 3), (3 X 4)},
  {(1 X 2), (1 X 5), (2 X 4), (2 X 5)},
  {(1 X 3), (1 X 4), (2 X 4), (2 X 5)}.

Crossrefs

Column k = 4 of A388143.

Cf. A387171.

Sequence in context: A014316 A389252 A075717 * A062487 A084447 A357290

Adjacent sequences: A384721 A384722 A384723 * A384725 A384726 A384727

Keyword

nonn

Author

Janaka Rodrigo, Aug 23 2025

Status

approved