A393105 a(n) is the maximum total surface area of five-element sets of distinct integer-sided cuboids that fill an n X n X n cube.

94, 184, 300, 456, 630, 832, 1062, 1340, 1628, 1944, 2288, 2660, 3150, 3584, 4046, 4536, 5054, 5600, 6174, 6776, 7406, 8064

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 surface areas

Example

According to A384479(4) there are 31 sets cuboids in total that fill 4 X 4 X 4 cube and only one set produces the maximum total surface area, {(1 X 1 X 4), (1 X 2 X 4), (1 X 3 X 4), (1 X 4 X 4), (2 X 3 X 4)} with total area 184. Therefore a(4) = 184 since the maximum total area of five cuboids is 184.

Crossrefs

Column 5 of A393319.

Cf. A384479, A385154, A393104, A384311, A392884, A385153, A392885.

Sequence in context: A050208 A035117 A096755 * A050965 A044426 A044807

Adjacent sequences: A393102 A393103 A393104 * A393106 A393107 A393108

Keyword

nonn,more

Author

Janaka Rodrigo, Feb 01 2026

Extensions

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

Status

approved