

A219158


Minimum number of integersided squares needed to tile an m by n rectangle.


15



1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 4, 4, 5, 1, 6, 3, 2, 3, 5, 1, 7, 5, 5, 5, 5, 5, 1, 8, 4, 5, 2, 5, 4, 7, 1, 9, 6, 3, 6, 6, 3, 6, 7, 1, 10, 5, 6, 4, 2, 4, 6, 5, 6, 1, 11, 7, 6, 6, 6, 6, 6, 6, 7, 6, 1, 12, 6, 4, 3, 6, 2, 6, 3, 4, 5, 7, 1, 13, 8, 7, 7, 6, 6, 6, 6, 7, 7, 6, 7, 1
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OFFSET

1,2


COMMENTS

Triangular array read by rows. m=1,2,...,n; n=1,2,3,...


LINKS

David Radcliffe, Rows n = 1..350 of triangle, flattened, computed by Massimo Ortolano using a C++ program written by Bertram Felgenhauer.
Gary Antonick, Matt Enlow's Rectangle Division Puzzle, The New York Times, June 15, 2015.
Bertram Felgenhauer, Filling rectangles with integersided squares
Richard J. Kenyon, Tiling a rectangle with the fewest squares, Combin. Theory Ser. A 76 (1996), no. 2, 272291.
M. Ortolano, M. Abrate, and L. Callegaro, On the synthesis of Quantum Hall Array Resistance Standards, arXiv preprint arXiv:1311.0756 [physics.insdet], 2013.
Mark Walters, Rectangles as sums of squares, Discrete Math. 309 (2009), no. 9, 29132921.


EXAMPLE

T(6,5) = 5 because a 6 X 5 rectangle can be subdivided into two 3 X 3 squares and three 2 X 2 squares.
Triangle begins:
: 1;
: 2, 1;
: 3, 3, 1;
: 4, 2, 4, 1;
: 5, 4, 4, 5, 1;
: 6, 3, 2, 3, 5, 1;
: 7, 5, 5, 5, 5, 5, 1;
: 8, 4, 5, 2, 5, 4, 7, 1;
: 9, 6, 3, 6, 6, 3, 6, 7, 1;
: 10, 5, 6, 4, 2, 4, 6, 5, 6, 1;
: 11, 7, 6, 6, 6, 6, 6, 6, 7, 6, 1;
: 12, 6, 4, 3, 6, 2, 6, 3, 4, 5, 7, 1;
: 13, 8, 7, 7, 6, 6, 6, 6, 7, 7, 6, 7, 1;
: 14, 7, 7, 5, 7, 5, 2, 5, 7, 5, 7, 5, 7, 1;
: 15, 9, 5, 7, 3, 4, 8, 8, 4, 3, 7, 5, 8, 7, 1;


CROSSREFS

First 19 terms agree with A049834.
Columns m=1..10 give A001477, A030451, A226576, A226577, A226578, A226579, A226580, A226581, A226582, A226583.
Cf. A113881, A338861.
Sequence in context: A180975 A210216 A195915 * A049834 A134625 A325477
Adjacent sequences: A219155 A219156 A219157 * A219159 A219160 A219161


KEYWORD

nonn,tabl


AUTHOR

David Radcliffe, Nov 12 2012


STATUS

approved



