A221845 Number of prime dissections of an n X n square into integer-sided squares.

1, 1, 5, 38, 471, 10661, 450923, 35863932, 5353011030, 1500957421749, 790347882174803, 781621363452395224, 1451740730942350766747, 5064070747064013555843107, 33176273260130056822126522407

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..15.

Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420

Example

For n = 3 the a(3) = 5 dissections are:
+-+-+-+   +-+-+-+   +-+-+-+   +-+---+   +---+-+
| | | |   | | | |   | | | |   | |   |   |   | |
+-+-+-+   +-+-+-+   +-+-+-+   +-+   |   |   +-+
| | | |   | |   |   |   | |   | |   |   |   | |
+-+-+-+   +-+   |   |   +-+   +-+-+-+   +-+-+-+
| | | |   | |   |   |   | |   | | | |   | | | |
+-+-+-+   +-+---+   +---+-+   +-+-+-+   +-+-+-+

Crossrefs

Cf. A045846, A221844.

Sequence in context: A216858 A338867 A110467 * A299054 A095230 A247708

Adjacent sequences: A221842 A221843 A221844 * A221846 A221847 A221848

Keyword

nonn

Author

Geoffrey H. Morley, Jan 26 2013

Extensions

Corrected and extended to a(15) by Geoffrey H. Morley, Feb 05 2013

Status

approved