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, 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

Author

Antoine Beaulieu, Dec 29 2021

Keywords

• nonn

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).

Examples

			|‾‾‾‾‾‾‾‾‾‾‾|
|           |
|     5     |
|           |        a(7)=12
|___________||‾‾‾|
|‾‾‾‾‾‾‾‾||_||___|
|    4   ||‾‾‾‾‾‾|
|        ||  3   |
|________||______|
|       7        |
.
.
               |‾‾‾‾‾‾|
|‾‾‾‾‾‾‾‾‾‾‾‾‾||   3  |      a(10)=15
|             ||      ||‾|
|       6     ||‾‾‾‾‾‾‾‾‾|
|             ||    4    |
|             ||         |
|_____________||_________|
|           10           |
		

Links

• Pontus von Brömssen, A350417(61) = 226.

Crossrefs

Cf. A295130.

Extensions

a(19) corrected by, a(21) and beyond from Pontus von Brömssen, Nov 15 2022