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 A386756 #9 Aug 03 2025 23:12:55
%S A386756 0,0,2,10,43,81,177,260,458,605,931,1169,1656,1995,2687,3145,4063,
%T A386756 4674,5850,6617,8102,9044,10852,12008,14172,15540,18116,19714,22711,
%U A386756 24585,28035,30176,34142,36569,41053,43817,48852,51939,57593,61021,67291,71118,78036,82241,89882
%N A386756 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 cube-shaped cuboids.
%C A386756 Alternatively, a(n) is the number of ways to decompose a (n,n,n) triplet into sets of four unordered triplets of the form (x,y,z) without having x=y=z in any of the triplets.
%e A386756 There are 12 sets of distinct four-cuboid combinations filling 4 X 4 X 4 cube according to A384311(4), only two combinations containing cubes listed below,
%e A386756 {(1,1,1), (1,1,3), (1,3,4), (3,4,4)},
%e A386756 {(1,3,3), (3,3,3), (1,3,4), (1,4,4)}.
%e A386756 Therefore, a(4) = 12-2 = 10.
%Y A386756 Cf. A384311.
%K A386756 nonn
%O A386756 1,3
%A A386756 _Janaka Rodrigo_, Aug 01 2025