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A384486 Table read by rows: number of connected components of polyhedra in the quarter cubic honeycomb consisting of k tetrahedra and n-k truncated tetrahedra, up to translation, rotation, and reflection of the honeycomb, 0<=k<=n.

%I A384486 #15 Jun 12 2025 14:07:42
%S A384486 1,1,1,1,1,0,1,3,1,0,3,8,8,1,0,7,31,43,14,1,0,24,126,261,152,18,0,0,
%T A384486 88,598,1543,1467,369,14,0,0,385,2986,9276,12161,5661,602,8,0,0,1713,
%U A384486 15467,55426,92723,65892,15251,694,3,0,0,8112,81217,330821,666705,646974,254615,29830,551,1,0,0
%N A384486 Table read by rows: number of connected components of polyhedra in the quarter cubic honeycomb consisting of k tetrahedra and n-k truncated tetrahedra, up to translation, rotation, and reflection of the honeycomb, 0<=k<=n.
%C A384486 Row sums are A384274.
%H A384486 Bert Dobbelaere, <a href="/A384486/b384486.txt">Table of n, a(n) for n = 0..119</a>
%H A384486 Wikipedia, <a href="https://en.wikipedia.org/wiki/Quarter_cubic_honeycomb">Quarter cubic honeycomb</a>
%H A384486 Peter Kagey, <a href="/A384486/a384486.pdf">Illustration of row 4</a>.
%F A384486 T(n,0) = A038169(n).
%e A384486 Table begins:
%e A384486  n\k|  0    1     2     3    4   5  6  7
%e A384486 ----+------------------------------------
%e A384486   0 |  1;
%e A384486   1 |  1,   1;
%e A384486   2 |  1,   1,    0;
%e A384486   3 |  1,   3,    1,    0;
%e A384486   4 |  3,   8,    8,    1,   0;
%e A384486   5 |  7,  31,   43,   14,   1,  0;
%e A384486   6 | 24, 126,  261,  152,  18,  0, 0;
%e A384486   7 | 88, 598, 1543, 1467, 369, 14, 0, 0;
%Y A384486 Cf. A038169, A384274.
%Y A384486 Cf. A365970 (tetrahedral-octahedral honeycomb).
%K A384486 nonn,tabl
%O A384486 0,8
%A A384486 _Peter Kagey_, May 30 2025
%E A384486 More terms from _Bert Dobbelaere_, Jun 12 2025