This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385580 #32 Aug 18 2025 03:03:19
%S A385580 0,0,4,11,47,77,183,259,457,599,941,1120,1668,1986,2637,3125,4079,
%T A385580 4622,5868,6530,8061,9028,10874,11856,14148,15522,18074,19583,22739,
%U A385580 24292,28065,30105,34071,36544,40885,43520,48888,51912,57512,60666,67331,70777,78078
%N A385580 a(n) is the number of ways to partition an n X n X n cube with four noncongruent cuboids of different volumes.
%C A385580 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.
%H A385580 Sean A. Irvine, <a href="/A385580/b385580.txt">Table of n, a(n) for n = 1..200</a>
%F A385580 Conjecture: a(p) = A384311(p) for any prime p.
%e A385580 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.
%Y A385580 Cf. A384311.
%K A385580 nonn
%O A385580 1,3
%A A385580 _Janaka Rodrigo_, Aug 12 2025