A393267 Array read by descending antidiagonals T(n,k) is the minimum total surface area of k-element sets of distinct integer-sided cuboids that fill an n X n X n cube.

54, 72, 96, 78, 128, 150, 80, 136, 200, 216, 92, 138, 210, 288, 294, 100, 144, 212, 300, 392, 384, 0, 148, 218, 302, 406, 512, 486, 0, 170, 222, 304, 408, 528, 648, 600, 0, 180, 228, 312, 410, 530, 666, 800, 726, 0, 194, 238, 318, 418, 532, 668, 820, 968, 864

Offset

3,1

Comments

The total surface area of k-element sets of cuboids is the sum of surface area of 2*(x*y+y*z+z*x) of each cuboid x X y X z in a set of distinct k cuboids.

Links

Table of n, a(n) for n=3..57.

Formula

T(n,1) = 6*n^2.

T(n,2) = 8*n^2 for n > 2.

T(n,3) = 2*n*(4*n+1) for n > 2.

Example

Array begins:
  54    72    78    80    92 ...
  96   128   136   138   144
 150   200   210   212   218
 216   288   300   302   304
 294   392   406   408   410
 384   512   528   530   532
 486   648   666   668   670
 600   800   820   822   824
 724   968   990   992   994
 864  1152  1176  1178  1180
 ...

Crossrefs

Cf. A033581 (k = 1), A139098 (k = 2), A033585 (k = 3), A392884 (k = 4), A393104 (k = 5).

Sequence in context: A350886 A281920 A005129 * A039532 A007244 A365262

Adjacent sequences: A393264 A393265 A393266 * A393268 A393269 A393270

Keyword

tabl,nonn

Author

Janaka Rodrigo, Feb 07 2026

Extensions

More terms from Sean A. Irvine, Feb 12 2026

Status

approved