A393104 - OEIS

%I #20 Feb 12 2026 15:01:10

%S 92,144,218,304,410,532,670,824,994,1180,1382,1600,1834,2084,2350,

%T 2632,2930,3244,3574,3920,4282,4660

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

%C The total surface area of five-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.

%H Janaka Rodrigo, <a href="/A393104/a393104.pdf">Five-Cuboid sets of A384479(4) with total area</a>

%F Conjecture: a(n) = 2*(A054567(n+1) + 1).

%e According to A384479(4) there are 31 sets of cuboids in total that fill 4 X 4 X 4 cube, and only one set produces the minimum total surface area, {(1 X 1 X 1), (1 X 1 X 2), (1 X 1 X 4), (1 X 3 X 3), (3 X 4 X 4)} with total area 145. Therefore a(4) = 144 since the minimum total area of five cuboids is 144.

%Y Column 5 of A393267.

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

%K nonn,more

%O 3,1

%A _Janaka Rodrigo_, Feb 01 2026

%E a(18)-a(24) from _Sean A. Irvine_, Feb 06 2026