login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 1
1, 2, 6, 15, 42, 143, 399, 1190, 4209, 10920, 37245, 109886, 339745, 1037186, 3205734, 9784263, 29837784, 93313919 (list; graph; refs; listen; history; text; internal format)
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(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

LINKS

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.

EXAMPLE

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 |

          |         |       |       |

          +---------+-------+-------+

.

CROSSREFS

Cf. A219158, A290821 (analog with triangles), A340920.

Sequence in context: A065178 A178936 A221744 * A340726 A303833 A148438

Adjacent sequences:  A338858 A338859 A338860 * A338862 A338863 A338864

KEYWORD

nonn,hard,more,changed

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)