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 A360943 #26 Mar 01 2023 08:12:07 %S A360943 0,0,0,0,0,0,360,0,360,360,8547192,0 %N A360943 Number of ways to tile an n X n square using rectangles with distinct dimensions where no rectangle has an edge length that divides n. %C A360943 All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 2 x 3 rectangle can only be used once, regardless of if it lies horizontally or vertically. %C A360943 Other known values are a(14) = 517344, a(15) = 6068760, a(16) = 339312. a(13) is greater than 800 million. %e A360943 a(1)..a(6),a(8),a(12) = 0 as these squares cannot be tiled with distinct rectangles with edge lengths that do not divide n. For example for the 8 x 8 square only three rectangles are available with dimensions 3 x 3, 3 x 5, and 5 x 5. All other rectangles have an edge length that divides 8 else leave a space of size 1 or 2 units between its edge and the edge of the square. These gaps cannot be filled as no rectangle can have an edge length of 1 or 2. %e A360943 a(7) = 360. And example tiling is: %e A360943 . %e A360943 +---+---+---+---+---+---+---+ %e A360943 | | | | %e A360943 + + + + %e A360943 | | | | %e A360943 +---+---+---+---+---+ + %e A360943 | | | %e A360943 + + + %e A360943 | | | %e A360943 +---+---+---+---+---+---+---+ %e A360943 | | | %e A360943 + + + %e A360943 | | | %e A360943 + + + %e A360943 | | | %e A360943 +---+---+---+---+---+---+---+ %e A360943 . %Y A360943 Cf. A360499, A360804, A360256, A360773, A182275, A004003. %K A360943 nonn,more %O A360943 1,7 %A A360943 _Scott R. Shannon_, Mar 01 2023