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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.

%I A350417 #24 Nov 17 2022 10:02:30
%S A350417 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,
%T A350417 56,63,61,71,71,82,82,90,83,96,95,108,99,108,111,127,102,146,144,130,
%U A350417 150,150,161,144,160,175,173,186,162,183,179,200,182,202,197,226
%N 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.
%C A350417 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).
%H A350417 Pontus von Brömssen, <a href="/A350417/a350417.svg">A350417(61) = 226</a>.
%e A350417 |‾‾‾‾‾‾‾‾‾‾‾|
%e A350417 |           |
%e A350417 |     5     |
%e A350417 |           |        a(7)=12
%e A350417 |___________||‾‾‾|
%e A350417 |‾‾‾‾‾‾‾‾||_||___|
%e A350417 |    4   ||‾‾‾‾‾‾|
%e A350417 |        ||  3   |
%e A350417 |________||______|
%e A350417 |       7        |
%e A350417 .
%e A350417 .
%e A350417                |‾‾‾‾‾‾|
%e A350417 |‾‾‾‾‾‾‾‾‾‾‾‾‾||   3  |      a(10)=15
%e A350417 |             ||      ||‾|
%e A350417 |       6     ||‾‾‾‾‾‾‾‾‾|
%e A350417 |             ||    4    |
%e A350417 |             ||         |
%e A350417 |_____________||_________|
%e A350417 |           10           |
%Y A350417 Cf. A295130.
%K A350417 nonn
%O A350417 1,2
%A A350417 _Antoine Beaulieu_, Dec 29 2021
%E A350417 a(19) corrected by, a(21) and beyond from _Pontus von Brömssen_, Nov 15 2022