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A210517 Number of rectangles dissectable into n squares. 1
1, 1, 2, 5, 11, 28, 76 (list; graph; refs; listen; history; text; internal format)



The rectangles are distinguishable by aspect ratio, not size.

A rectangle is dissectable into squares if and only if its sides are commensurable. A rectangle with commensurable sides is dissectable into n squares for all but a finite number of positive integers n. For example, a square is dissectable into any number of squares other than 2, 3, or 5.


Table of n, a(n) for n=1..7.


For n = 3 the a(3) = 2 rectangles are 3X1 and 3X2. For example, a 3X2 rectangle can be tiled by a 2X2 square and two 1X1 squares.

For n = 4 the a(4) = 5 rectangles are 1X1, 4X1, 4X3, 5X2 and 5X3.

For n = 5 the a(5) = 11 rectangles are 2X1, 5X1, 5X4, 6X5, 7X2, 7X3, 7X4, 7X5, 7X6, 8X3 and 8X5.

For n = 6 the a(6) = 28 rectangles are 1X1, 3X1, 3X2, 4X3, 5X4, 6X1, 6X5, 9X2, 9X4, 9X5, 9X7, 10X3, 10X7, 10X9, 11X3, 11X4, 11X5, 11X6, 11X7, 11X8, 11X10, 12X5, 12X7, 13X5, 13X6, 13X7, 13X8 and 13X11.


Cf. A221839.

Sequence in context: A121398 A000625 A202476 * A244531 A288390 A127331

Adjacent sequences:  A210514 A210515 A210516 * A210518 A210519 A210520




Geoffrey H. Morley, Jan 26 2013



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Last modified September 19 18:37 EDT 2020. Contains 337181 sequences. (Running on oeis4.)