A387241 a(n) is the number of 5 element sets of distinct integer sided rectangles that fill an n X n square.

0, 0, 0, 2, 19, 87, 257, 571, 1186, 2033, 3488, 5272, 8131, 11320, 16327, 21497, 29397, 37399, 49133, 60616, 77485, 93373, 116367, 137941, 168441, 196548, 236397, 272238, 322686, 368109, 430896, 486803, 564461, 632419, 726311, 808688, 921012, 1018824, 1152744, 1267811, 1424860, 1560243, 1742966, 1899610, 2111980

Offset

1,4

Comments

Determining the number of sets of five distinct unordered integer sided rectangles that fill an n X n square is done by decomposing the pair (n,n) into five unordered integer pairs of distinct composition under two categories to find two sequences of sets R(n) and K(n). Sets generated by binary space partitioning are given by R(n) and sets generated without allowing a single cut going through the full square are given by K(n).

Since some sets are common in both categories: a(n) = |R(n) union K(n)|.

Links

Table of n, a(n) for n=1..45.

Janaka Rodrigo, Sequence of sets R(n)

Janaka Rodrigo, Sequence of sets K(n)

Example

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

Crossrefs

Column 5 of A385240.

Cf. A384479 (3-dimensional version), A387171 (4 elements).

Sequence in context: A331898 A054570 A135436 * A387605 A056005 A034572

Adjacent sequences: A387238 A387239 A387240 * A387242 A387243 A387244

Keyword

nonn

Author

Janaka Rodrigo, Aug 23 2025

Status

approved