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A221844 Number of prime dissections of an n X n square into integer sided squares up to symmetry. 2
1, 1, 2, 11, 76, 1490, 56977, 4495010, 669203525 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

J. H. Conway, Mrs Perkins's quilt, Proc. Camb. Phil. Soc., 60 (1964), 363-368.

LINKS

Table of n, a(n) for n=1..9.

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

4X4     3X3     2X2     1X1    (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

Cf. A221843, A221845.

Sequence in context: A118802 A053481 A110329 * A006766 A120380 A079266

Adjacent sequences:  A221841 A221842 A221843 * A221845 A221846 A221847

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

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Last modified July 24 16:49 EDT 2017. Contains 289775 sequences.