cp's OEIS Frontend

A384756 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 translation and rotation, 0 <= k <= n.

%I A384756 #16 Jun 14 2025 17:16:33
%S A384756 1,1,1,1,2,1,3,8,11,2,14,60,118,63,5,88,575,1457,1372,368,16,686,5741,
%T A384756 18261,24831,13581,2124,59,5966,59088,225424,403494,339880,117447,
%U A384756 12201,250,54722,616110,2745525,6084433,6987036,3927441,926001,69445,1136
%N A384756 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 translation and rotation, 0 <= k <= n.
%H A384756 Bert Dobbelaere, <a href="/A384756/b384756.txt">Table of n, a(n) for n = 0..65</a>
%H A384756 Peter Kagey, <a href="/A384756/a384756.png">Illustration of row 3</a>.
%H A384756 Peter Kagey, Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/282216/53884">Putting the pieces together</a>.
%H A384756 Wikipedia, <a href="https://en.wikipedia.org/wiki/Convex_uniform_honeycomb">Convex uniform honeycomb</a>
%F A384756 T(n,0)=A038170(n).
%e A384756   |   0     1      2      3      4     5   6
%e A384756 --+------------------------------------------
%e A384756 0 |   1;
%e A384756 1 |   1,    1;
%e A384756 2 |   1,    2,     1;
%e A384756 3 |   3,    8,    11,     2;
%e A384756 4 |  14,   60,   118,    63,     5;
%e A384756 5 |  88,  575,  1457,  1372,   368,   16;
%e A384756 6 | 686, 5741, 18261, 24831, 13581, 2124, 59;
%Y A384756 Cf. A384755 (rotation and reflection).
%K A384756 nonn,tabl
%O A384756 0,5
%A A384756 _Peter Kagey_, Jun 09 2025
%E A384756 More terms from _Bert Dobbelaere_, Jun 14 2025