A385580 a(n) is the number of ways to partition an n X n X n cube into four noncongruent cuboids of different volumes.

0, 0, 4, 11, 47, 77, 183, 259, 457, 599, 941, 1120, 1668, 1986, 2637, 3125, 4079, 4622, 5868, 6530, 8061, 9028, 10874, 11856, 14148, 15522, 18074, 19583, 22739, 24292, 28065, 30105, 34071, 36544, 40885, 43520, 48888, 51912, 57512, 60666, 67331, 70777, 78078

Offset

1,3

Comments

Alternatively, a(n) is the number of ways to decompose (n,n,n) triplet into geometrically feasible four distinct unordered triplets of the form (x,y,z) with no pairs of triplets having equal value for the product x*y*z.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..200

Formula

Conjecture: a(p) = A384311(p) for any prime p.

Example

There are A384311(4) = 12 different ways to decompose a 4 X 4 X 4 cube into four noncongruent cuboids, but of those 12 ways, one partition {(4,2,1), (4,2,2), (4,3,2), (4,4,1)} contains two cuboids of volume 16 ((4,2,2) and (4,4,1)) which needs to be excluded. Therefore a(4) = 12-1 = 11.

Crossrefs

Column 4 of A387121.

Cf. A384311.

Sequence in context: A149302 A149303 A053882 * A246652 A393154 A254202

Adjacent sequences: A385577 A385578 A385579 * A385581 A385582 A385583

Keyword

nonn

Author

Janaka Rodrigo, Aug 12 2025

Status

approved