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.
Bertram Felgenhauer, Filling rectangles with integer-sided squares
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
KEYWORD
nonn,tabl
AUTHOR
David Radcliffe, Nov 12 2012
STATUS
approved