

A002962


Number of simple imperfect squared squares of order n up to symmetry.
(Formerly M2496)


8



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
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OFFSET

1,15


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 (20102012). 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

Table of n, a(n) for n=1..32.
Stuart Anderson, Simple Imperfect Squared Squares.
A. J. W. Duijvestijn, Electronic Computation of Squared Rectangles, Thesis, Technische Hogeschool, Eindhoven, Netherlands, 1962. Reprinted in Philips Res. Rep., 17 (1962), 523612. [Pp. 5734 have simple imperfect squares up to order 19.]
Index entries for squared squares


CROSSREFS

Cf. A006983, A002881, A002839, A014530.
Cf. A181735, A217155, A217156.
Sequence in context: A054432 A016043 A077403 * A220164 A018374 A063185
Adjacent sequences: A002959 A002960 A002961 * A002963 A002964 A002965


KEYWORD

nonn,hard,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected a(19), extended terms up to a(22), Stuart Anderson, Mar 08 2011
Corrected a(21), a(22), extended terms to a(25), Stuart Anderson, Apr 24 2011
Corrected a(21), a(22), a(25), added a(26), a(27), a(28), Stuart Anderson, Jul 11 2011
Added a(29), Stuart Anderson, Ed Pegg Jr, Stephen Johnson, Aug 22 2011
Corrected a(29) Stuart 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
Added a(30), by Lorenz Milla and Stuart E Anderson, Apr 10 2013
a(26) and a(29) corrected by Stuart E Anderson, Aug 20 2013
a(31) and a(32) added by Lorenz Milla and Stuart E Anderson, Sep 30 2013


STATUS

approved



