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A221844
Number of prime dissections of an n X n square into integer-sided squares up to symmetry.
3
1, 1, 2, 11, 76, 1490, 56977, 4495010, 669203525
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.
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
Sequence in context: A053481 A368794 A110329 * A006766 A120380 A369542
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