A389716 - OEIS

%I #23 Feb 24 2026 08:21:39

%S 84,152,240,360,490,640,810,1000,1210,1440,1690,1960,2250,2560,2890,

%T 3240,3610,4000,4410,4840,5290,5760,6250,6760,7290,7840,8410,9000,

%U 9610,10240,10890,11560,12250,12960,13690,14440,15210,16000,16810,17640,18490,19360,20250

%N a(n) is the maximum total surface area of three-element sets of distinct integer-sided cuboids that fill an n X n X n cube.

%C Total surface area of three-element sets of cuboids is given by the sum of surface area 2*(x*y+y*z+z*x) of each cuboid x X y X z in the set.

%e According to the column 3 of A386296, there are 3 sets of cuboids in total that fill 4 X 4 X 4 cube and only one set produces the maximum total surface area:

%e  {(4 X 3 X 3), (4 X 3 X 1), (4 X 4 X 1)} with total area 152,

%e  {(4 X 4 X 3), (4 X 3 X 1), (4 X 1 X 1)} with total area 136,

%e  {(4 X 4 X 2), (4 X 3 X 2), (4 X 2 X 1)} with total area 144.

%e Therefore a(4) = 152 since the maximum total surface area of three cuboids is 152.

%Y Column 3 of A393319.

%Y Cf. A386296, A381847, A384311, A392884, A385153, A392885, A384479, A385154, A393104, A393105.

%K nonn

%O 3,1

%A _Janaka Rodrigo_, Feb 06 2026