cp's OEIS Frontend

A386903 Array read by descending antidiagonals: T(n,k) is the number of ways to partition n X n X n cube into k noncongruent strict cuboids, n>=5, k>=4.

%I A386903 #17 Aug 20 2025 19:15:09
%S A386903 1,0,2,3,18,9,1,64,74,12,1,143,450,193,30,0,197,2090,1769,491,36,0,
%T A386903 156,8039,13441,5687,857,70,0,57,24641,88001,56540,12994,1695,80,0,5
%N A386903 Array read by descending antidiagonals: T(n,k) is the number of ways to partition n X n X n cube into k noncongruent strict cuboids, n>=5, k>=4.
%C A386903 A strict cuboid is a cuboid with all dimensions different.
%C A386903 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, x != y != z and volume x*y*z.
%C A386903 There are no solutions for n < 5 or k < 4.
%e A386903 Array begins:
%e A386903   n\k|  4     5      6       7      8      9
%e A386903   ---+--------------------------------------
%e A386903    5 |  1     0      3       1      1      0
%e A386903    6 |  2    18     64     143    197    156
%e A386903    7 |  9    74    450    2090   8039  24641
%e A386903    8 | 12   193   1769   13441  88001      ?
%e A386903    9 | 30   491   5687   56540      ?      ?
%e A386903   10 | 36   857  12994  170052      ?      ?
%e A386903   ...
%Y A386903 Cf. A386296.
%Y A386903 Columns: A386884 (k=4), A386902 (k=5).
%K A386903 tabl,nonn,more
%O A386903 5,3
%A A386903 _Janaka Rodrigo_, Aug 07 2025