A393104 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.

92, 144, 218, 304, 410, 532, 670, 824, 994, 1180, 1382, 1600, 1834, 2084, 2350, 2632, 2930, 3244, 3574, 3920, 4282, 4660

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..24.

Janaka Rodrigo, Five-Cuboid sets of A384479(4) with total area

Formula

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

Example

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.

Crossrefs

Column 5 of A393267.

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

Sequence in context: A387999 A273286 A257761 * A393599 A252067 A182266

Adjacent sequences: A393101 A393102 A393103 * A393105 A393106 A393107

Keyword

nonn,more

Author

Janaka Rodrigo, Feb 01 2026

Extensions

a(18)-a(24) from Sean A. Irvine, Feb 06 2026

Status

approved