A220164 Number of simple squared squares of order n up to symmetry.

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

Offset: 1

Author

Stuart E Anderson, Dec 06 2012

Keywords

• nonn
• hard

Comments

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.

References

• See A006983 and A217156.

Links

• 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

Crossrefs

Cf. A006983, A002962, A217156, A089046.

Formula

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

Extensions

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