OFFSET
1,1
COMMENTS
Some notations: s = side of the tiled squares, a = side of small squares, b = side of large squares, and z = number of small squares = number of large squares.
Every term is of the form z = (a*b)^2 * (a^2+b^2) with gcd(a, b) = 1.
Every primitive square is composed of m = a*b * (a^2+b^2) elementary rectangles of length L = a^2+b^2 and width W = a*b, so with an area A = a*b * (a^2+b^2) = m.
This sequence is not increasing: a(9) = 2450 < a(8) = 3600.
Every term is even.
If a = 1 and b = n > 1, then number of squares z = n^2 * (n^2+1) is in A071253 \ {0,2}.
REFERENCES
Ivan Yashchenko, Invitation to a Mathematical Festival, pp. 10 and 102, MSRI, Mathematical Circles Library, 2013.
EXAMPLE
Square 10 x 10 with a = 1, b = 2, s = 10, z = 20.
___ ___ _ ___ ___ _
| | |_| | |_|
|___|___|_|___|___|_|
| | |_| | |_| with 10 elementary 2 x 5 rectangles
|___|___|_|___|___|_|
| | |_| | |_| ___ ___ _
|___|___|_|___|___|_| | | |_|
| | |_| | |_| |___|___|_|
|___|___|_|___|___|_|
| | |_| | |_|
|___|___|_|___|___|_|
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jun 02 2021
STATUS
approved