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A219158 Minimum number of integer-sided squares needed to tile an m X n rectangle. 17
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Triangular array read by rows. m=1,2,...,n; n=1,2,3,...
LINKS
Massimo Ortolano, Table of n, a(n) for n = 1..75466, rows 1..388 of triangle, flattened. Corrected version provided by Qizheng He.
Gary Antonick, Matt Enlow's Rectangle Division Puzzle, The New York Times, June 15, 2015.
Richard J. Kenyon, Tiling a rectangle with the fewest squares, Combin. Theory Ser. A 76 (1996), no. 2, 272-291.
M. Ortolano, M. Abrate, and L. Callegaro, On the synthesis of Quantum Hall Array Resistance Standards, arXiv preprint arXiv:1311.0756 [physics.ins-det], 2013.
Mark Walters, Rectangles as sums of squares, Discrete Math. 309 (2009), no. 9, 2913-2921.
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.
Sequence in context: A180975 A210216 A195915 * A049834 A134625 A325477
KEYWORD
nonn,tabl
AUTHOR
David Radcliffe, Nov 12 2012
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)