A002962 Number of simple imperfect 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, 274, 491, 1766, 3679, 11158, 24086, 64754, 132598, 326042, 667403, 1627218, 3508516

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

Comments

A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of squares. If no two of these squares have the same size the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares. - Geoffrey H. Morley, Oct 17 2012

Orders 15 to 19 were enumerated by C. J. Bowkamp and A. J. W. Duijvestijn (1962). Orders 20 to 29 were enumerated by Stuart Anderson (2010-2012). Orders 30 to 32 were enumerated by Lorenz Milla and Stuart Anderson (2013). - Stuart E Anderson, Sep 30 2013

References

• C. J. Bouwkamp, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Stuart Anderson, Simple Imperfect Squared Squares.
• C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
• A. J. W. Duijvestijn, Electronic Computation of Squared Rectangles, Thesis, Technische Hogeschool, Eindhoven, Netherlands, 1962. Reprinted in Philips Res. Rep., 17 (1962), 523-612. [Pp. 573-4 have simple imperfect squares up to order 19.]
• Index entries for squared squares

Crossrefs

Cf. A002839, A002881, A006983, A014530.

Cf. A181735, A217155, A217156.

Extensions

a(19) corrected and terms extended up to a(22) by Stuart E Anderson, Mar 08 2011

a(21) and a(22) corrected and terms extended to a(25) by Stuart E Anderson, Apr 24 2011

a(21), a(22), a(25) corrected and a(26)-a(28) added by Stuart E Anderson, Jul 11 2011

a(29) from Stuart E Anderson, Ed Pegg Jr, Stephen Johnson, Aug 22 2011

a(29) corrected by Stuart E Anderson, Aug 24 2011

Definition clarified and offset changed to 1 by Geoffrey H. Morley, Oct 17 2012

a(28) corrected by Stuart E Anderson, Dec 01 2012

a(30) from Lorenz Milla and Stuart E Anderson, Apr 10 2013

a(26) and a(29) corrected by Stuart E Anderson, Aug 20 2013

a(31), a(32) from Lorenz Milla and Stuart E Anderson, Sep 30 2013