cp's OEIS Frontend

A384755 Triangle read by rows: T(n,k) is the number of face-connected components of polyhedra with k prisms and n-k truncated cuboctahedra in the omnitruncated cubic honeycomb up to rotation and reflection, 0 <= k <= n.

%I A384755 #17 Jun 14 2025 17:16:25
%S A384755 1,1,1,1,2,1,3,7,10,2,12,41,76,46,4,61,335,809,777,232,13,407,3065,
%T A384755 9512,12863,7186,1206,39,3226,30401,114516,204143,172377,60421,6548,
%U A384755 155,28335,311782,1381363,3054599,3507278,1975767,469525,36081,637,262091,3260971,16569719,43731912
%N A384755 Triangle read by rows: T(n,k) is the number of face-connected components of polyhedra with k prisms and n-k truncated cuboctahedra in the omnitruncated cubic honeycomb up to rotation and reflection, 0 <= k <= n.
%C A384755 Row sums are A384754.
%H A384755 Bert Dobbelaere, <a href="/A384755/b384755.txt">Table of n, a(n) for n = 0..65</a>
%H A384755 Peter Kagey, <a href="/A384755/a384755.png">Illustration of row 3</a>.
%H A384755 Wikipedia, <a href="https://en.wikipedia.org/wiki/Convex_uniform_honeycomb">Convex uniform honeycomb</a>
%F A384755 T(n,0) = A038171(n).
%e A384755 0 |   1;
%e A384755 1 |   1,    1;
%e A384755 2 |   1,    2,    1;
%e A384755 3 |   3,    7,   10,     2;
%e A384755 4 |  12,   41,   76,    46,    4;
%e A384755 5 |  61,  335,  809,   777,  232,   13;
%e A384755 6 | 407, 3065, 9512, 12863, 7186, 1206, 39;
%Y A384755 Cf. A038171, A384754, A384756.
%Y A384755 Cf. A365970 (tetrahedral-octahedral honeycomb), A384486 (quarter cubic honeycomb), A384782 (rectified cubic honeycomb).
%K A384755 nonn,tabl
%O A384755 0,5
%A A384755 _Peter Kagey_, Jun 09 2025
%E A384755 More terms from _Bert Dobbelaere_, Jun 14 2025