This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385151 #34 Jul 16 2025 23:34:56
%S A385151 6,24,20,48,42,80,54,140,99,192,143,252,150,352,238,432,304,520,294,
%T A385151 660,437,768,525,884,486,1064,696,1200,806,1344,726,1564,1015,1728,
%U A385151 1147,1900,1014,2160,1394,2352,1548,2552,1350,2852,1833,3072,2009,3300,1734
%N A385151 a(n) is the least possible difference between the largest and smallest volumes of distinct three-cuboid combination filling an n X n X n cube.
%C A385151 Developed as the three dimensional extension of the Mondrian Art Problem.
%C A385151 Alternatively, a(n) is the optimal solution when an n X n X n cube is partitioning into 3 cuboids of different dimensions.
%C A385151 Let elements of the unordered integer triplet (x,y,z) be the dimensions of cuboid in a set of three cuboids.
%C A385151 Let V(x,y,z) = x*y*z be the volume and for a given set of triplets S, Min(S) = min{V(x,y,z):(x,y,z) in S}, Max(S) = max{V(x,y,z):(x,y,z) in S}, and defect(S) = Max(S)-Min(S).
%C A385151 a(n) is the least possible value of the defect as S runs over the possible partitions of the n X n X n cuboid into 3 cuboids of different dimensions.
%H A385151 Janaka Rodrigo, <a href="/A385151/a385151.txt">Python program</a>
%e A385151 4 X 4 X 4 cube can be partitioned in three different ways and defects of sets are calculated as follows:
%e A385151 {(4,3,3), (4,3,1), (4,4,1)}: defect = max(36,12,16)-min(36,12,16) = 36-12=24,
%e A385151 {(4,2,1), (4,3,2), (4,4,2)}: defect = max(8,24,32)-min(8,24,32) = 32-8=24,
%e A385151 {(4,4,3), (4,3,1), (4,1,1)}: defect = max(48,12,4)-min(48,12,4) = 48-4=44.
%e A385151 Therefore, a(4) = min{24, 24, 44} = 24.
%Y A385151 Cf. A276523, A381847.
%K A385151 nonn
%O A385151 3,1
%A A385151 _Janaka Rodrigo_, Jun 19 2025