login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A350417
a(n) is the maximum number of rows of width n that can be filled by stacking squares of sizes 1 through n without creating voids or overhangs.
1
1, 2, 4, 5, 7, 8, 12, 12, 16, 15, 20, 24, 26, 25, 30, 29, 35, 33, 40, 40, 47, 46, 61, 51, 73, 56, 63, 61, 71, 71, 82, 82, 90, 83, 96, 95, 108, 99, 108, 111, 127, 102, 146, 144, 130, 150, 150, 161, 144, 160, 175, 173, 186, 162, 183, 179, 200, 182, 202, 197, 226
OFFSET
1,2
COMMENTS
No square of any size can be used more than once. The initial terms listed are conjectured from what I can draw. Trying to stack squares in this way feels like playing Tetris and comes from the squared square idea (see A295130).
LINKS
EXAMPLE
|‾‾‾‾‾‾‾‾‾‾‾|
| |
| 5 |
| | a(7)=12
|___________||‾‾‾|
|‾‾‾‾‾‾‾‾||_||___|
| 4 ||‾‾‾‾‾‾|
| || 3 |
|________||______|
| 7 |
.
.
|‾‾‾‾‾‾|
|‾‾‾‾‾‾‾‾‾‾‾‾‾|| 3 | a(10)=15
| || ||‾|
| 6 ||‾‾‾‾‾‾‾‾‾|
| || 4 |
| || |
|_____________||_________|
| 10 |
CROSSREFS
Cf. A295130.
Sequence in context: A191174 A261188 A343267 * A176193 A072920 A330708
KEYWORD
nonn
AUTHOR
Antoine Beaulieu, Dec 29 2021
EXTENSIONS
a(19) corrected by, a(21) and beyond from Pontus von Brömssen, Nov 15 2022
STATUS
approved