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 A386902 #14 Aug 29 2025 04:28:47
%S A386902 0,0,0,0,0,18,74,193,491,857,1695,2503,4321,5836,9200,11715,17284,
%T A386902 21256,29805,35589,48156,56260,73766,84860,108495,123080,154298,
%U A386902 172998,213045,236895,287260,316743,379465,415456,491930,535713,627879,680052,790401,851914,982130
%N A386902 a(n) is the number of distinct five-cuboid combinations that fill an n X n X n with only strict cuboids.
%C A386902 A strict cuboid is a cuboid with all three dimensions different.
%C A386902 Alternatively a(n) is the number of ways to decompose (n,n,n) triplet into set of geometrically feasible distinct five unordered triplets of the form (x,y,z) with x != y != z for each of five triplets.
%e A386902 (6,6,6) triplet can be decomposed into set of five triplets in 560 different ways and only 18 of those formed by only strict cuboids. Three of those sets are given below:
%e A386902 {(1,2,3), (1,3,4), (2,3,6), (3,4,6), (3,5,6)},
%e A386902 {(1,2,6), (1,4,6), (2,4,6), (2,5,6), (3,4,6)},
%e A386902 {(1,3,4), (1,3,6), (2,3,5), (2,3,6), (4,5,6)}.
%Y A386902 Cf. A384479, A386847.
%K A386902 nonn,changed
%O A386902 1,6
%A A386902 _Janaka Rodrigo_, Aug 07 2025
%E A386902 a(16)-a(18) from _Sean A. Irvine_, Aug 14 2025
%E A386902 More terms from _Jinyuan Wang_, Aug 29 2025