A387598 a(n) is the number of 3 element sets of distinct integer sided strict rectangles that fill an n X n square.

0, 0, 0, 1, 4, 7, 13, 17, 27, 32, 45, 52, 68, 76, 96, 105, 128, 139, 165, 177, 207, 220, 253, 268, 304, 320, 360, 377, 420, 439, 485, 505, 555, 576, 629, 652, 708, 732, 792, 817, 880, 907, 973, 1001, 1071, 1100, 1173, 1204, 1280, 1312

Offset

1,5

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

Formula

From Andrew Howroyd, Sep 03 2025: (Start)

a(n) = floor((n - 1)/2)*(n - 3) + round((n - 3)^2/12).

G.f.: x^4*(1 + 4*x + 5*x^2 + 4*x^3)/((1 - x)^3*(1 + x)^2*(1 + x + x^2)). (End)

Example

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

Crossrefs

Column k = 3 of A388143.

Cf. A001399, A381847.

Sequence in context: A310822 A265704 A110267 * A049698 A288823 A310823

Adjacent sequences: A387595 A387596 A387597 * A387599 A387600 A387601

Keyword

nonn,easy

Author

Janaka Rodrigo, Sep 02 2025

Status

approved