A210517 Number of rectangles dissectible into n squares, unique up to aspect ratio.
1, 1, 2, 5, 11, 28, 74, 211
Offset: 1
Examples
For n = 3 the a(3) = 2 rectangles are 3 X 1 and 3 X 2 with aspect ratio 3/1 and 3/2. For example, a 3 X 2 rectangle can be tiled by a 2 X 2 square and two 1 X 1 squares. For n = 4 the a(4) = 5 aspect ratios are 1/1, 4/1, 4/3, 5/2 and 5/3. Ratio 1/1 stems from the square 2 X 2, tiled by four 1 X 1 squares. For n = 5 the a(5) = 11 aspect ratios are 2/1, 5/1, 5/4, 6/5, 7/2, 7/3, 7/4, 7/5, 7/6, 8/3 and 8/5. For n = 6 the a(6) = 28 aspect ratios are 1/1, 3/1, 3/2, 4/3, 5/4, 6/1, 6/5, 9/2, 9/4, 9/5, 9/7, 10/3, 10/7, 10/9, 11/3, 11/4, 11/5, 11/6, 11/7, 11/8, 11/10, 12/5, 12/7, 13/5, 13/6, 13/7, 13/8 and 13/11.
Links
- Rainer Rosenthal, SetA210517(n) = set of aspect ratios for n squares (for n < 9).
Extensions
Title changed by Rainer Rosenthal, Dec 30 2022
a(7) corrected, a(8) new. - Marx Stampfli and Rainer Rosenthal, Jan 10 2023
Comments