A389716 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.

84, 152, 240, 360, 490, 640, 810, 1000, 1210, 1440, 1690, 1960, 2250, 2560, 2890, 3240, 3610, 4000, 4410, 4840, 5290, 5760, 6250, 6760, 7290, 7840, 8410, 9000, 9610, 10240, 10890, 11560, 12250, 12960, 13690, 14440, 15210, 16000, 16810, 17640, 18490, 19360, 20250

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..45.

Example

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:
 {(4 X 3 X 3), (4 X 3 X 1), (4 X 4 X 1)} with total area 152,
 {(4 X 4 X 3), (4 X 3 X 1), (4 X 1 X 1)} with total area 136,
 {(4 X 4 X 2), (4 X 3 X 2), (4 X 2 X 1)} with total area 144.
Therefore a(4) = 152 since the maximum total surface area of three cuboids is 152.

Crossrefs

Column 3 of A393319.

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

Sequence in context: A101260 A141502 A039499 * A341128 A055712 A066292

Adjacent sequences: A389713 A389714 A389715 * A389717 A389718 A389719

Keyword

nonn

Author

Janaka Rodrigo, Feb 06 2026

Status

approved