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%I #31 Sep 06 2021 04:29:35
%S 1,1,2,11,76,1490,56977,4495010,669203525
%N Number of prime dissections of an n X n square into integer-sided squares up to symmetry.
%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.
%H J. H. Conway, <a href="http://dx.doi.org/10.1017/S0305004100037877">Mrs. Perkins's quilt</a>, 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>, 2013, arXiv:1308.5420
%e For n = 4 there are a(4) = 11 dissections:
%e +-+-+-+-+ +---+-+-+ +-+---+-+ +-+-+-+-+ +---+---+ +---+-+-+
%e | | | | | | | | | | | | | | | | | | | | | | | | |
%e +-+-+-+-+ | +-+-+ +-+ +-+ +-+-+-+-+ | | | | +-+-+
%e | | | | | | | | | | | | | | | | | | | | | | |
%e +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+ +-+ +-+-+-+-+ +-+-+ |
%e | | | | | | | | | | | | | | | | | | | | | | | | | | | |
%e +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+
%e | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
%e +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+
%e ...
%e +---+-+-+ +-+---+-+ +---+---+ +---+---+ +-----+-+
%e | | | | | | | | | | | | | | | | |
%e | +-+-+ +-+ +-+ | | | | | | | +-+
%e | | | | | | | | | | | | | | | | |
%e +-+-+-+-+ +-+---+-+ +---+-+-+ +-+-+-+-+ | +-+
%e | | | | | | | | | | | | | | | | | | |
%e +-+-+ | +-+ +-+ | +-+-+ +-+ +-+ +-+-+-+-+
%e | | | | | | | | | | | | | | | | | | | | |
%e +-+-+---+ +-+---+-+ +---+-+-+ +-+---+-+ +-+-+-+-+
%e ...
%e For n = 5 there are a(5) = 76 dissections, each of which comprises one of A221843(5) = 10 sets of subsquares:
%e .
%e Subsquares Prime dissections
%e 4 X 4 3 X 3 2 X 2 1 X 1 (up to symmetry)
%e ----- ----- ----- ----- ----------------
%e - - - 25 1
%e - - 1 21 3
%e - - 2 17 13
%e - - 3 13 20
%e - - 4 9 14
%e - 1 - 16 3
%e - 1 1 12 6
%e - 1 2 8 10
%e - 1 3 4 5
%e 1 - - 9 1
%e --
%e 76
%Y Cf. A221843, A221845.
%K nonn,more
%O 1,3
%A _Geoffrey H. Morley_, Jan 26 2013
%E More terms from Wynn, 2013. - _N. J. A. Sloane_, Nov 29 2013
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