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 A387040 #11 Aug 29 2025 04:54:59
%S A387040 0,0,2,26,206,442,1531,2661,5574,8514,15614,20331,34500,44814,64503,
%T A387040 83143,117759,141290,193436,226722,295978,351953,447208,507508,637447,
%U A387040 732322,887044,1001577,1213233,1337525,1611692,1786560,2088648,2321052,2673275,2929254,3404667
%N A387040 a(n) is the number of distinct five-cuboid combinations that fill an n X n X n cube with cuboids of different volumes.
%C A387040 Alternatively a(n) is the number of ways to decompose (n,n,n) triplet into geometrically feasible five distinct unordered triplets of the form (x,y,z) with no pair having equal value for the product x*y*z.
%e A387040 According to A384479(5), (5,5,5) triplet can be decomposed into 209 distinct sets of five triplets and only three of them contain pair of triplets with equal value for x*y*z. Those are,
%e A387040 {(1,2,5), (1,3,5), (1,4,5), (2,2,5), (3,4,5)},
%e A387040 {(1,1,5), (1,4,5), (2,2,5), (2,3,5), (2,5,5)},
%e A387040 {(1,3,5), (1,4,5), (2,2,5), (2,3,5), (2,4,5)}.
%e A387040 Therefore a(5) = 209-3 = 206.
%Y A387040 Cf. A384479, A385580, A387121.
%K A387040 nonn,changed
%O A387040 1,3
%A A387040 _Janaka Rodrigo_, Aug 14 2025
%E A387040 a(15)-a(16) from _Sean A. Irvine_, Aug 19 2025
%E A387040 More terms from _Jinyuan Wang_, Aug 29 2025