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A386757 a(n) is the number of sets of noncongruent five-cuboid combinations that fill an n X n X n cube excluding combinations that contain cube-shaped cuboids.

%I A386757 #21 Aug 04 2025 10:13:27
%S A386757 0,0,1,21,179,513,1471,2736,5713,8881,15478,21961,34355,45696,66768,
%T A386757 84922,117621,145313,193283,232787,300764,355093,447181,520412,641801,
%U A386757 736900,894222,1015173,1213646,1366103,1612366,1799756,2102572,2329955,2695421,2970037,3406356
%N A386757 a(n) is the number of sets of noncongruent five-cuboid combinations that fill an n X n X n cube excluding combinations that contain cube-shaped cuboids.
%C A386757 Alternatively a(n) is the number of ways to decompose (n,n,n) triplet into sets of distinct five unordered triplets of the form (x,y,z) without having x = y = z in any of the triplets.
%e A386757 There are 31 sets of distinct unordered five-cuboid combinations filling 4 X 4 X 4 cube including 10 combinations containing cube-shaped cuboids which are listed below,
%e A386757    {(1,1,1), (1,1,2), (1,1,4), (1,3,3), (3,4,4)},
%e A386757    {(1,1,1), (1,1,2), (1,3,3), (1,4,4), (3,3,4)},
%e A386757    {(1,1,1), (1,1,3), (1,1,4), (1,2,4), (3,4,4)},
%e A386757    {(1,1,1), (1,1,3), (1,1,4), (2,3,4), (2,4,4)},
%e A386757    {(1,1,1), (1,1,3), (1,2,4), (1,4,4), (3,3,4)},
%e A386757    {(1,1,1), (1,1,3), (1,3,4), (1,4,4), (2,4,4)},
%e A386757    {(1,1,3), (1,2,3), (1,3,4), (1,4,4), (3,3,3)},
%e A386757    {(1,1,4), (1,2,4), (1,3,3), (1,4,4), (3,3,3)},
%e A386757    {(1,2,2), (1,2,4), (2,2,2), (2,2,3), (2,4,4)},
%e A386757    {(1,2,2), (1,4,4), (2,2,2), (2,2,3), (2,3,4)}.
%e A386757 Therefore a(4) = 31 - 10 = 21.
%Y A386757 Cf. A384479, A386779.
%K A386757 nonn
%O A386757 1,4
%A A386757 _Janaka Rodrigo_, Aug 01 2025
%E A386757 a(14)-a(16) from _Sean A. Irvine_, Aug 03 2025
%E A386757 a(17)-a(37) from _Jinyuan Wang_, Aug 04 2025