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A220164 Number of simple squared squares of order n up to symmetry. 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 5, 15, 19, 57, 72, 275, 499, 1778, 3705, 11318, 24525, 65906, 135599, 333938, 687969, 1681759, 3652677 (list; graph; refs; listen; history; text; internal format)



A squared rectangle is a rectangle dissected into a finite number, two or more, of squares, called the elements of the dissection. If no two of these squares have the same size the squared rectangle is called perfect, otherwise it is imperfect. The order of a squared rectangle is the number of constituent squares. The case in which the squared rectangle is itself a square is called a squared square. The dissection is simple if it contains no smaller squared rectangle, otherwise it is compound. This sequence counts both perfect and imperfect simple squared squares up to symmetry.


See A006983 and A217156.


Table of n, a(n) for n=1..32.

S. E. Anderson, Simple Perfect Squared Squares

S. E. Anderson, Simple Imperfect Squared Squares

S. E. Anderson, Mrs Perkins's Quilts

Eric Weisstein's World of Mathematics, Perfect Square Dissection


a(n) = A006983(n) + A002962(n).


Cf. A006983, A002962, A217156, A089046.

Sequence in context: A016043 A077403 A002962 * A018374 A290297 A063185

Adjacent sequences:  A220161 A220162 A220163 * A220165 A220166 A220167




Stuart E Anderson, Dec 06 2012


a(13)-a(29) from Stuart E Anderson, Dec 07 2012

Clarified some definitions in comments and added a(30) - Stuart E Anderson, Jun 03 2013

a(31), a(32) added by Stuart E Anderson, Sep 30 2013



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Last modified August 6 08:39 EDT 2020. Contains 336228 sequences. (Running on oeis4.)