OFFSET
1,2
COMMENTS
See (Gambini, 1999) for a way to construct the sequence. Actually, one would have to extend Gambini's idea by putting extra 1-sided squares in the list of "usable squares" to allow finding nonzero-waste packings.
LINKS
Vitor Pimenta dos Reis Arruda, Table of n, a(n) for n = 1..101
I. Gambini, A method for cutting squares into distinct squares, Discrete Applied Mathematics, 98 (1999), 65-80.
Vitor Pimenta dos Reis Arruda, Non trivial decompositions until a(101)
Vitor Pimenta dos Reis Arruda, Luiz Gustavo Bizarro Mirisola, and Nei Yoshihiro Soma, Almost squaring the square: optimal packings for non-decomposable squares, Pesqui. Oper. (2022) Vol. 42.
Giovanni Resta, Illustration of terms a(15)-a(31)
Wikipedia, Squaring the square
EXAMPLE
For n=5, squares of sides {1, 4} can be packed inside the container, leading to uncovered area a(5) = 5*5 - (4*4 + 1*1) = 8. The other maximal packable set is composed of the squares sided {1,2,3}, which would lead to uncovered area greater than 8.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vitor Pimenta dos Reis Arruda, May 15 2020
EXTENSIONS
Terms a(17)-a(31) from Giovanni Resta, May 15 2020
STATUS
approved