OFFSET
1,3
COMMENTS
A dissection into squares was called prime by J. H. Conway in 1964 if the GCD of the sides of the squares is 1.
LINKS
J. H. Conway, Mrs. Perkins's quilt, Proc. Camb. Phil. Soc., 60 (1964), 363-368.
Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, 2013, arXiv:1308.5420
EXAMPLE
For n = 4 there are a(4) = 11 dissections:
+-+-+-+-+ +---+-+-+ +-+---+-+ +-+-+-+-+ +---+---+ +---+-+-+
| | | | | | | | | | | | | | | | | | | | | | | | |
+-+-+-+-+ | +-+-+ +-+ +-+ +-+-+-+-+ | | | | +-+-+
| | | | | | | | | | | | | | | | | | | | | | |
+-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+ +-+ +-+-+-+-+ +-+-+ |
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
+-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
+-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+
...
+---+-+-+ +-+---+-+ +---+---+ +---+---+ +-----+-+
| | | | | | | | | | | | | | | | |
| +-+-+ +-+ +-+ | | | | | | | +-+
| | | | | | | | | | | | | | | | |
+-+-+-+-+ +-+---+-+ +---+-+-+ +-+-+-+-+ | +-+
| | | | | | | | | | | | | | | | | | |
+-+-+ | +-+ +-+ | +-+-+ +-+ +-+ +-+-+-+-+
| | | | | | | | | | | | | | | | | | | | |
+-+-+---+ +-+---+-+ +---+-+-+ +-+---+-+ +-+-+-+-+
...
For n = 5 there are a(5) = 76 dissections, each of which comprises one of A221843(5) = 10 sets of subsquares:
.
Subsquares Prime dissections
4 X 4 3 X 3 2 X 2 1 X 1 (up to symmetry)
----- ----- ----- ----- ----------------
- - - 25 1
- - 1 21 3
- - 2 17 13
- - 3 13 20
- - 4 9 14
- 1 - 16 3
- 1 1 12 6
- 1 2 8 10
- 1 3 4 5
1 - - 9 1
--
76
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Geoffrey H. Morley, Jan 26 2013
EXTENSIONS
More terms from Wynn, 2013. - N. J. A. Sloane, Nov 29 2013
STATUS
approved