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A338861
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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.
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1
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1, 2, 6, 15, 42, 143, 399, 1190, 4209, 10920, 37245, 109886, 339745, 1037186, 3205734, 9784263, 29837784, 93313919
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OFFSET
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1,2
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COMMENTS
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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(18) have to be considered only as lower bounds: a(19) >= 289627536, a(20) >= 876696755, a(21) >= 2735106696. - Hugo Pfoertner, Nov 17 2020, Feb 18 2021
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LINKS
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Table of n, a(n) for n=1..18.
Stuart Anderson, Catalogues of Simple Perfect Squared Rectangles.
Stuart Anderson, Simple Imperfect Squared Rectangles, orders 9 to 24.
Bertram Felgenhauer, Filling rectangles with integer-sided squares.
MathOverflow, tiling a rectangle with the smallest number of squares, answer by Ed Pegg Jr, Jul 09 2017.
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EXAMPLE
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Dissection of the 11 X 13 rectangle into 6 squares:
+-----------+-------------+
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| 6 X 6 | 7 X 7 |
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+---------+-+ |
| +-+-----+-------+
| 5 X 5 | | |
| | 4 X 4 | 4 X 4 |
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+---------+-------+-------+
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CROSSREFS
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Cf. A219158, A290821 (analog with triangles), A340920.
Sequence in context: A065178 A178936 A221744 * A340726 A303833 A148438
Adjacent sequences: A338858 A338859 A338860 * A338862 A338863 A338864
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KEYWORD
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nonn,hard,more,changed
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AUTHOR
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Rainer Rosenthal, Nov 12 2020
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EXTENSIONS
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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
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STATUS
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approved
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