This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360256 #55 Jun 26 2025 13:02:25 %S A360256 1,1,33,513,14409,693025,50447161 %N A360256 Number of ways to tile an n X n square using rectangles with distinct height X width dimensions. %C A360256 All possible tilings are counted, including those identical by symmetry. Note that distinct height X width dimensions means that, for example, a 1 X 3 rectangle can be used twice, once in a horizontal (1 X 3) and once in a vertical (3 X 1) direction. %e A360256 a(1) = 1 as the only way to tile a 1 X 1 square is with a square with dimensions 1 X 1. %e A360256 a(2) = 1 as the only way to tile a 2 X 2 square is with a square with dimensions 2 X 2. %e A360256 a(3) = 33. The possible tilings, excluding those equivalent by symmetry, are: %e A360256 . %e A360256 +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ %e A360256 | | | | | | | | | | | | | | %e A360256 +---+---+---+ +---+---+---+ +---+---+ + +---+---+---+ +---+---+---+ %e A360256 | | | | | | | | | | | | | %e A360256 + + + + + + + + + + + + + %e A360256 | | | | | | | | | | | | | %e A360256 +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ %e A360256 . %e A360256 The first tiling can occur in 4 different ways, the second in 8 different ways, the third in 8 different ways, the fourth in 4 different ways and the fifth in 8 different ways. There is also the single 3 X 3 rectangle. This gives 33 ways in total. %Y A360256 Cf. A360725 (oblongs), A360499, A360498, A182275, A004003, A099390, A065072. %K A360256 nonn,more %O A360256 1,3 %A A360256 _Scott R. Shannon_, Feb 17 2023