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.

1, 1, 1, 1, 2, 1, 3, 8, 11, 2, 14, 60, 118, 63, 5, 88, 575, 1457, 1372, 368, 16, 686, 5741, 18261, 24831, 13581, 2124, 59, 5966, 59088, 225424, 403494, 339880, 117447, 12201, 250, 54722, 616110, 2745525, 6084433, 6987036, 3927441, 926001, 69445, 1136

Offset: 0

Author

Peter Kagey, Jun 09 2025

Keywords

• nonn
• tabl

Examples

			  |   0     1      2      3      4     5   6
--+------------------------------------------
0 |   1;
1 |   1,    1;
2 |   1,    2,     1;
3 |   3,    8,    11,     2;
4 |  14,   60,   118,    63,     5;
5 |  88,  575,  1457,  1372,   368,   16;
6 | 686, 5741, 18261, 24831, 13581, 2124, 59;
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 0..65
• Peter Kagey, Illustration of row 3.
• Peter Kagey, Code Golf Stack Exchange, Putting the pieces together.
• Wikipedia, Convex uniform honeycomb

Crossrefs

Cf. A384755 (rotation and reflection).

Formula

T(n,0)=A038170(n).

Extensions

More terms from Bert Dobbelaere, Jun 14 2025