

A338861


a(n) is the largest area of a rectangle which can be dissected into n squares with integer sides s_i, i = 1 .. n, and gcd(s_1,...,s_n) = 1.


3



1, 2, 6, 15, 42, 143, 399, 1190, 4209, 10920, 37245, 109886, 339745, 1037186, 3205734, 9784263, 29837784, 93313919, 289627536
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OFFSET

1,2


COMMENTS

A219158 gives the minimum number of squares to tile an i x j rectangle. a(n) is found by checking all rectangles (i,j) for which A219158 has a dissection into n squares.
Due to the potential counterexamples to the minimal squaring conjecture (see MathOverflow link), terms after a(19) have to be considered only as lower bounds: a(20) >= 876696755, a(21) >= 2735106696.  Hugo Pfoertner, Nov 17 2020, Apr 02 2021


LINKS

Table of n, a(n) for n=1..19.
Stuart Anderson, Catalogues of Simple Perfect Squared Rectangles.
Stuart Anderson, Simple Imperfect Squared Rectangles, orders 9 to 24.
Bertram Felgenhauer, Filling rectangles with integersided squares.
MathOverflow, tiling a rectangle with the smallest number of squares, answer by Ed Pegg Jr, Jul 09 2017.
Rainer Rosenthal, Rectangle tiled by 19 squares with maximum area a(19)


EXAMPLE

a(6) = 11*13 = 143.
Dissection of the 11 X 13 rectangle into 6 squares:
.
+++
  
  
 6 X 6  7 X 7 
  
  
+++ 
 ++++
 5 X 5   
  4 X 4  4 X 4 
   
++++
.
a(19) = 16976*17061 = 289627536.
Dissection of the 16976 X 17061 rectangle into 19 squares:
.
+++
  
  7849 
 9212  
  
 ___________
_____________  
  see  4109 
 link  
 7764 ____+++
   5018 
 4279 
++++
.


CROSSREFS

Cf. A219158, A290821 (analog with triangles), A340726, A340920.
Sequence in context: A065178 A178936 A221744 * A340726 A303833 A148438
Adjacent sequences: A338858 A338859 A338860 * A338862 A338863 A338864


KEYWORD

nonn,hard,more


AUTHOR

Rainer Rosenthal, Nov 12 2020


EXTENSIONS

a(11)a(17) from Hugo Pfoertner based on data from squaring.net website, Nov 17 2020
a(18) from Hugo Pfoertner, Feb 18 2021
a(19) from Hugo Pfoertner, Apr 02 2021


STATUS

approved



