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 A386846 #12 Aug 06 2025 21:34:48
%S A386846 0,0,2,3,4,6,6,9,8,13,11,17,15,23,20,30,27,39,36,50,47,64,61,80,78,
%T A386846 100,98,123,122,150,150,181,182,217,219,257,261,303,308,354,361,411,
%U A386846 420,474,485,544,557,620,636,704,722,795,816,894,918,1001,1028,1117
%N A386846 a(n) is the number of sets of distinct four-cuboid combinations that fill an n X n X n cube excluding combinations that contain strict cuboids.
%C A386846 A strict cuboid is a cuboid with all three dimensions different to each other.
%C A386846 Alternatively a(n) is number of ways to decompose (n,n,n) triplet into sets of distinct unordered geometrically feasible four triplets of the form (x,y,z) excluding x != y != z in any of the triplets.
%e A386846 (5,5,5) triplet can be decomposed into sets of four triplets in 47 different ways and only the following 4 sets do not contain strict cuboids.
%e A386846 {(5,5,1), (5,4,4), (4,1,1), (1,4,4)},
%e A386846 {(5,5,3), (5,2,2), (3,3,2), (2,2,3)},
%e A386846 {(5,5,2), (3,3,5), (2,2,3), (3,3,2)},
%e A386846 {(4,1,1), (5,1,1), (1,4,4), (4,5,5)}.
%Y A386846 Cf. A384311.
%K A386846 nonn
%O A386846 1,3
%A A386846 _Janaka Rodrigo_, Aug 05 2025
%E A386846 More terms from _Sean A. Irvine_, Aug 06 2025