A221844 Number of prime dissections of an n X n square into integer-sided squares up to symmetry.
1, 1, 2, 11, 76, 1490, 56977, 4495010, 669203525
Offset: 1
Examples
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 4 X 4 3 X 3 2 X 2 1 X 1 (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
Links
- J. H. Conway, Mrs. Perkins's quilt, Proc. Camb. Phil. Soc., 60 (1964), 363-368.
- Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, 2013, arXiv:1308.5420
Extensions
More terms from Wynn, 2013. - N. J. A. Sloane, Nov 29 2013
Comments