A392885 a(n) is the maximum total surface area of four-element sets of distinct integer-sided cuboids that fill an n X n X n cube.

92, 170, 272, 408, 560, 736, 936, 1200, 1452, 1728, 2028, 2352, 2700, 3072, 3468, 3888, 4332, 4800, 5292, 5808, 6348, 6912, 7500, 8112, 8748, 9408, 10092, 10800, 11532, 12288, 13068, 13872, 14700, 15552, 16428, 17328, 18252, 19200, 20172, 21168, 22188, 23232, 24300

Offset

3,1

Comments

Total surface area of four-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..45.

Example

According to A384311(3) there are four sets of cuboids in total that fill 3 X 3 X 3 cube:
 {(3 X 3 X 2), (3 X 2 X 1), (2 X 1 X 1), (1 X 1 X 1)} with total area = 80,
 {(3 X 3 X 2), (3 X 1 X 1), (2 X 2 X 1), (2 X 1 X 1)} with total area = 82,
 {(3 X 3 X 1), (3 X 2 X 2), (2 X 2 X 1), (2 X 1 X 1)} with total area = 88,
 {(3 X 3 X 1), (3 X 2 X 1), (2 X 2 X 2), (2 X 2 X 1)} with total area = 92.
Therefore a(3) = 92 since the maximum total area of four cuboids is 92.

Crossrefs

Column 4 of A393319.

Cf. A384311, A392884, A385153.

Sequence in context: A393599 A252067 A182266 * A116215 A272369 A044424

Adjacent sequences: A392882 A392883 A392884 * A392886 A392887 A392888

Keyword

nonn

Author

Janaka Rodrigo, Jan 25 2026

Status

approved