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 A360499 #12 Feb 16 2023 11:31:59 %S A360499 1,1,21,269,4489,82981,2995185,118897973 %N A360499 Number of ways to tile an n X n square using rectangles with distinct dimensions. %C A360499 All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 1 x 3 rectangle can only be used once, regardless of if it lies horizontally or vertically. %e A360499 a(1) = 1 as the only way to tile a 1 x 1 square is with a square with dimensions 1 x 1. %e A360499 a(2) = 1 as the only way to tile a 2 x 2 square is with a square with dimensions 2 x 2. %e A360499 a(3) = 21. The possible tilings, excluding those equivalent by symmetry, are: %e A360499 . %e A360499 +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ %e A360499 | | | | | | | | | | %e A360499 + + +---+---+---+ +---+---+ + +---+---+---+ %e A360499 | | | | | | | | | %e A360499 + + + + + + + + + %e A360499 | | | | | | | | | %e A360499 +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ %e A360499 . %e A360499 The first tiling can occur in 1 way, the second in 8 different ways, the third in 8 different ways and the fourth in 4 different ways, giving 21 ways in total. %Y A360499 Cf. A360498 (oblongs), A182275 (not necessarily distinct dimensions), A004003, A099390, A065072, A233320, A230031. %K A360499 nonn,more %O A360499 1,3 %A A360499 _Scott R. Shannon_, Feb 09 2023