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

Author

Geoffrey H. Morley, Jan 26 2013

Keywords

• nonn

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.

Examples

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

References

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

Links

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

Crossrefs

Cf. A045846, A221844.

Extensions

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