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 A387121 #16 Aug 25 2025 19:13:09 %S A387121 1,0,1,0,0,1,0,0,1,1,0,0,2,1,1,0,0,4,3,2,1,0,0,2,11,8,2,1,0,0,1,26,47, %T A387121 11,3,1,0,0,0,55,206,77,19,3,1,0,0,0,48,793,442,183,23,4,1,0,0,0,23, %U A387121 2653,2451,1531,259,35,4,1,0,0,0,0,6706,13022,12178 %N A387121 Array read by antidiagonals: T(n,k) is the number of sets of k integer sided cuboids with distinct volumes that fill an n X n X n cube. %C A387121 The partitions here must be valid packings of the n X n X n cube, hence T(n,k) is generally less than the number of partitions of n^3 into distinct cuboids (x,y,z) with 1 <= x,y,z <= n and no pair of triplets having equal volume x*y*z. %F A387121 T(n,1) = 1, T(n,k) = 0 for k > n^3. %e A387121 Array begins: %e A387121 1 0 0 0 0 %e A387121 1 0 0 0 0 %e A387121 1 1 2 4 2 %e A387121 1 1 3 11 26 %e A387121 1 2 8 47 206 %e A387121 1 2 11 77 442 %e A387121 1 3 19 183 1531 %e A387121 1 3 23 259 2661 %e A387121 1 4 35 457 5574 %e A387121 1 4 40 599 8514 %e A387121 ... %Y A387121 Columns are A004526 (k=2), A381847 (k=3), A385580 (k=4), A387040 (k=5). %K A387121 tabl,nonn,new %O A387121 1,13 %A A387121 _Janaka Rodrigo_, Aug 16 2025 %E A387121 More terms from _Sean A. Irvine_, Aug 25 2025