A386297 - OEIS

A386297

Array read by antidiagonals T(n,k) is the minimal defect across all partitions of an n X n X n cube into k noncongruent cuboids, or 0 if there is no such partition.

9, 6, 32, 5, 24, 25, 10, 16, 20, 72, 8, 12, 16, 48, 49, 0, 12, 21, 36, 42, 128, 0, 12, 12, 28, 30, 80, 81, 0, 13, 12, 24, 28, 60, 54, 200, 0, 10, 16, 12, 24, 62, 48, 140, 121, 0, 15, 12, 18, 20, 41, 42, 100, 99, 288, 0, 0, 14, 12, 21, 26, 32, 80, 83, 192, 169

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

3,1

COMMENTS

Let V(x,y,z)=x*y*z be the volume of a cuboid (x,y,z). For a given set of cuboids S, define Min(S) = min{V(x,y,z): (x,y,z) in S}, Max(S)= max{V(x,y,z): (x,y,z) in S}, and defect = max(S)-min(S).

T(n, k) = min(defect(S)) as S runs over all partitions of an n X n X n cuboid into k noncongruent cuboids.

A386296 gives the number of sets S.

LINKS

Table of n, a(n) for n=3..68.

EXAMPLE

Array begins

9 6 5 10

32 24 16 12

25 20 16 21

72 48 36 28

49 42 30 28

128 80 60 62

81 54 48 42

200 140 100 80

The only set S of distinct six cuboids filling 3 X 3 X 3 cube in triplet form is, S = {(1,1,1), (1,1,2), (1,1,3), (1,2,2), (2,2,2), (1,3,3)} giving Min(S)=1, Max(S)=9, and defect(S) = 9-1 = 8. Since this is the only defect T(3,6)=8.

CROSSREFS

Cf. A081900, A385151, A385153, A385154, A386296.

Sequence in context: A156033 A196005 A196002 * A390835 A370151 A038296

Adjacent sequences: A386294 A386295 A386296 * A386298 A386299 A386300

KEYWORD

tabl,nonn

AUTHOR

Janaka Rodrigo, Jul 17 2025

EXTENSIONS

More terms from Sean A. Irvine, Jul 29 2025

STATUS

approved