A384743 - OEIS

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.

0, 0, 0, 1, 6, 20, 50, 110, 197, 343, 535, 814, 1171, 1651, 2240, 2996, 3900, 5019, 6333, 7918, 9744, 11905, 14366, 17225, 20451, 24146, 28274, 32955, 38143, 43967, 50380, 57520, 65335, 73976, 83386, 93720, 104925, 117165, 130377, 144743, 160190, 176909, 194831

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OFFSET

1,5

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..43.

Janaka Rodrigo, Sets of D(n)-A(n) in Triplets Form

EXAMPLE

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)}}.

B(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.

C(3) = {}.

D(3) = B(3) U C(3) = {{(1,1,2), (1,1,3), (1,2,2), (1,2,3), (2,2,3)}}.

D(3)-A(3) = {}.

Therefore, a(3) = 0.

CROSSREFS

Cf. A381847, A384208, A384311, A384479, A384737.