Search: a349210 -id:a349210
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A006983
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Number of simple perfect squared squares of order n up to symmetry.
(Formerly M4482)
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+10
29
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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, 20566, 54541, 144161, 378197, 990981, 2578081, 6674067, 17086918
(list;
graph;
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listen;
history;
text;
internal format)
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OFFSET
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1,22
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COMMENTS
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A squared rectangle (which may be a square) is a rectangle dissected into a finite number of two or more squares. If no two 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
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REFERENCES
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J.-P. Delahaye, Les inattendus mathématiques, Belin-Pour la Science, Paris, 2004, pp. 95-96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
A. J. W. Duijvestijn, Illustration for a(21)=1 (The unique simple squared square of order 21. Reproduced with permission of the discoverer.)
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CROSSREFS
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KEYWORD
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nonn,hard,more,nice
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AUTHOR
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EXTENSIONS
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Leading term changed from 0 to 1, Apr 15 1996
Leading term changed back to 0, Dec 25 2010 (cf. A178688)
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
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STATUS
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approved
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A349205
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a(n) is the side length (size) of the smallest element in a simple perfect squared square of order n such that the ratio of the size of the smallest element to the total size of the square assumes a maximum over all possible A006983(n) dissections of order n.
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+10
7
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2, 4, 2, 3, 12, 17, 48, 29, 62, 53, 64, 156, 70, 270, 257, 333, 716
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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21,1
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LINKS
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EXAMPLE
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See Pfoertner link.
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CROSSREFS
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A349206 gives the corresponding total sizes of those squares that lead to the maximum ratio.
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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A349206
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a(n) is the side length of the simple perfect squared square of order n leading to a maximum of the ratio of the side length of its smallest element A349205(n) to its total side length.
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+10
7
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112, 192, 140, 120, 381, 544, 1032, 732, 1615, 1485, 1408, 3584, 1625, 6808, 6192, 7743, 16581
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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21,1
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LINKS
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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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A349207
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a(n) is the side length (size) of the smallest element in a simple perfect squared square of order n such that the ratio of the size of the smallest element to the size of the largest element of the square assumes a maximum over all possible A006983(n) dissections of order n.
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+10
7
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2, 4, 2, 3, 16, 17, 48, 29, 62, 69, 64, 88, 70, 111, 355, 333, 543
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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21,1
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LINKS
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EXAMPLE
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See Pfoertner link.
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CROSSREFS
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A349208 gives the corresponding sizes of the largest elements that lead to the maximum ratio.
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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A349209
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a(n) is the maximum of the side lengths of the smallest elements of all simple perfect squared squares of order n.
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+10
7
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2, 4, 2, 8, 16, 20, 48, 48, 69, 74, 107, 158, 177, 270, 355, 519, 716
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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21,1
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LINKS
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EXAMPLE
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See linked illustrations.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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A349208
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a(n) is the largest side length (size) of an element of the simple perfect squared square of order n leading to a maximum of the ratio of the size of its smallest element A349207(n) to the size of its largest element.
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+10
6
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50, 86, 60, 47, 195, 202, 457, 304, 591, 698, 520, 769, 549, 860, 3276, 2456, 4098
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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21,1
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LINKS
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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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