A385580 a(n) is the number of ways to partition an n X n X n cube with 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

Author

Janaka Rodrigo, Aug 12 2025

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A384311.

Formula

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