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

1,15

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

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

Formula

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

Crossrefs

Cf. A006983, A002962, A217156, A089046.

Sequence in context: A016043 A077403 A002962 * A018374 A290297 A344991

Adjacent sequences: A220161 A220162 A220163 * A220165 A220166 A220167

Keyword

nonn,hard

Author

Stuart E Anderson, Dec 06 2012

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

Status

approved