|
| |
|
|
A006983
|
|
Number of simple perfect squared squares of order n.
(Formerly M4482)
|
|
8
| |
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 12, 26, 160, 441, 1152, 3001, 7901
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,22
|
|
|
COMMENTS
| The order of a squared square is the number of squares into which it is divided.
The term 1152 was found by Jasper Skinner by exhaustive search of all c-nets of order 28.
The term 3001 was found by Stuart Anderson and Ed Pegg Jr after exhaustive search of all 29 edge 3-connected planar graphs (produced by McKay/Brinkmann's plantri software). Dissections from these and other orders can be viewed from the Anderson link.
|
|
|
REFERENCES
| C. J. Bouwkamp and A. J. W. Duijvestijn, Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25. Eindhoven Univ. Technology, Dept. of Math., Report 92-WSK-03, Nov. 1992.
C. J. Bouwkamp and A. J. W. Duijvestijn, Album of Simple Perfect Squared Squares of order 26, Eindhoven University of Technology, Faculty of Mathematics and Computing Science, EUT Report 94-WSK-02, December 1994.
A. J. W. Duijvestijn, J. Comb. Theory B 59 (1993), 26-34.
A. J. W. Duijvestijn, Math. Comp. 62 (1994), 325-332.
A. J. W. Duijvestijn, P. J. Federico and P. Leeuw, Compound perfect squares, American Mathematical Monthly 89 (1982), 15-32. - there is no compound perfect squared square of order < 24.
J.-P. Delahaye, Les inattendus mathematiques, pp. 95-6 Belin-Pour la Science Paris 2004.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| S. E. Anderson, Perfect Squared Rectangles and Squared Squares
C. J. Bouwkamp, On some new simple perfect squared squares, Disc. Math. 106-107 (1992) 67-75.
A. J. W. Duijvestijn, Illustration for a(21)=1 (The unique simple squared square of order 21. Reproduced with permission of the discoverer.)
A. J. W. Duijvestijn, Table I and Table II
A. J. W. Duijvestijn, Simple perfect squares and 2x1 squared rectangles of order 26, Math. Comp. 65 (1996) 1359-1364.
Eric Weisstein's World of Mathematics, Perfect Square Dissection
|
|
|
CROSSREFS
| Cf. A002962, A002881, A002839, A014530, A181735, A178688.
Sequence in context: A077566 A067677 A045523 * A072327 A181735 A161415
Adjacent sequences: A006980 A006981 A006982 * A006984 A006985 A006986
|
|
|
KEYWORD
| nonn,hard,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Leading term changed from 0 to 1 Apr 15 1996.
More terms from Stuart. E. Anderson, May 08 2003, Nov 2010.
Leading term changed back to 0, Dec 25 2010 (cf. A178688).
a(29) added by Stuart. E. Anderson, Aug 22 2010. Contributors to a(29) include Ed Pegg Jr and Stephen Johnson.
a(29) changed to 7901, identified a duplicate tiling in order 29. Stuart. E. Anderson, Jan 07 2012
a(28) changed to 3000, identified a duplicate tiling in order 28. Stuart. E. Anderson, Jan 14 2012
a(28) changed back to 3001 after a complete recount of order 28 SPSS recalculated from c-nets with cleansed data, established the correct total of 3001. Stuart. E. Anderson, Jan 24 2012
|
| |
|
|
