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A350417
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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|‾‾‾‾‾‾‾‾‾‾‾|
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| 5 |
| | a(7)=12
|___________||‾‾‾|
|‾‾‾‾‾‾‾‾||_||___|
| 4 ||‾‾‾‾‾‾|
| || 3 |
|________||______|
| 7 |
.
.
|‾‾‾‾‾‾|
|‾‾‾‾‾‾‾‾‾‾‾‾‾|| 3 | a(10)=15
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| 6 ||‾‾‾‾‾‾‾‾‾|
| || 4 |
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|_____________||_________|
| 10 |
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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