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

1,2

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

Table of n, a(n) for n=1..61.

Pontus von Brömssen, A350417(61) = 226.

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

Adjacent sequences: A350414 A350415 A350416 * A350418 A350419 A350420

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