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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 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 October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)