A221845 - OEIS

%I #20 Sep 05 2021 21:59:14

%S 1,1,5,38,471,10661,450923,35863932,5353011030,1500957421749,

%T 790347882174803,781621363452395224,1451740730942350766747,

%U 5064070747064013555843107,33176273260130056822126522407

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

%C A dissection into squares was called prime by _J. H. Conway_ in 1964 if the GCD of the sides of the squares is 1.

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

%H Ed Wynn, <a href="http://arxiv.org/abs/1308.5420">Exhaustive generation of Mrs Perkins's quilt square dissections for low orders</a>, arXiv:1308.5420

%e For n = 3 the a(3) = 5 dissections are:

%e +-+-+-+   +-+-+-+   +-+-+-+   +-+---+   +---+-+

%e | | | |   | | | |   | | | |   | |   |   |   | |

%e +-+-+-+   +-+-+-+   +-+-+-+   +-+   |   |   +-+

%e | | | |   | |   |   |   | |   | |   |   |   | |

%e +-+-+-+   +-+   |   |   +-+   +-+-+-+   +-+-+-+

%e | | | |   | |   |   |   | |   | | | |   | | | |

%e +-+-+-+   +-+---+   +---+-+   +-+-+-+   +-+-+-+

%Y Cf. A045846, A221844.

%K nonn

%O 1,3

%A _Geoffrey H. Morley_, Jan 26 2013

%E Corrected and extended to a(15) by _Geoffrey H. Morley_, Feb 05 2013