cp's OEIS Frontend

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.

A361413 Number of ways to tile an n X n square using rectangles with distinct dimensions where all the rectangle edge lengths are prime numbers.

This page as a plain text file.
%I A361413 #8 Mar 11 2023 23:07:12
%S A361413 0,1,1,0,1,0,1,0,0,4128,1,10880,641,45904,349496,892088,40873,17695080
%N A361413 Number of ways to tile an n X n square using rectangles with distinct dimensions where all the rectangle edge lengths are prime numbers.
%C A361413 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 whether it lies horizontally or vertically.
%e A361413 a(2), a(3), a(5), a(7), a(11) = 1 as the only possible tiling is that using an n X n square where n is a prime number. It is likely 11 is the last prime indexed term that equals 1 although this is unknown.
%e A361413 a(10) = 4128. And example tiling is:
%e A361413 .
%e A361413   +---+---+---+---+---+---+---+---+---+---+
%e A361413   |       |           |                   |
%e A361413   +       +           +                   +
%e A361413   |       |           |                   |
%e A361413   +---+---+---+---+---+---+---+---+---+---+
%e A361413   |           |                           |
%e A361413   +           +                           +
%e A361413   |           |                           |
%e A361413   +           +                           +
%e A361413   |           |                           |
%e A361413   +---+---+---+                           +
%e A361413   |           |                           |
%e A361413   +           +                           +
%e A361413   |           |                           |
%e A361413   +           +---+---+---+---+---+---+---+
%e A361413   |           |                           |
%e A361413   +           +                           +
%e A361413   |           |                           |
%e A361413   +           +                           +
%e A361413   |           |                           |
%e A361413   +---+---+---+---+---+---+---+---+---+---+
%e A361413 .
%Y A361413 Cf. A360943, A360499, A360804, A360256, A360773, A182275, A004003.
%K A361413 nonn,more
%O A361413 1,10
%A A361413 _Scott R. Shannon_, Mar 10 2023