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A384743 a(n) is the number of distinct five-cuboid combinations filling n X n X n cube without allowing a cut spanning through the full cube in any of filling positions.

%I A384743 #19 Aug 04 2025 14:29:11
%S A384743 0,0,0,1,6,20,50,110,197,343,535,814,1171,1651,2240,2996,3900,5019,
%T A384743 6333,7918,9744,11905,14366,17225,20451,24146,28274,32955,38143,43967,
%U A384743 50380,57520,65335,73976,83386,93720,104925,117165,130377,144743,160190,176909,194831
%N A384743 a(n) is the number of distinct five-cuboid combinations filling n X n X n cube without allowing a cut spanning through the full cube in any of filling positions.
%C A384743 Alternatively a(n) is the number of distinct five-triplet sets of the terms produced by D(n)-A(n); that is, a(n) = |D(n)-A(n)|, where A(n), B(n) and C(n) are introduced in A384479 and D(n) = B(n) U C(n).
%H A384743 Janaka Rodrigo, <a href="/A384743/a384743.pdf">Sets of D(n)-A(n) in Triplets Form</a>
%e A384743 A(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}, {(1,1,1), (1,1,2), (1,1,3), (1,3,3), (2,2,3)}}.
%e A384743 B(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.
%e A384743 C(3) = {}.
%e A384743 D(3) = B(3) U C(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.
%e A384743 D(3)-A(3) = {}.
%e A384743 Therefore, a(3) = 0.
%Y A384743 Cf. A381847, A384208, A384311, A384479, A384737.
%K A384743 nonn
%O A384743 1,5
%A A384743 _Janaka Rodrigo_, Jun 08 2025
%E A384743 a(11)-a(43) from _Jinyuan Wang_, Aug 04 2025