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.

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, 88, 598, 1543, 1467, 369, 14, 0, 0, 385, 2986, 9276, 12161, 5661, 602, 8, 0, 0, 1713, 15467, 55426, 92723, 65892, 15251, 694, 3, 0, 0, 8112, 81217, 330821, 666705, 646974, 254615, 29830, 551, 1, 0, 0

Offset: 0

Author

Peter Kagey, May 30 2025

Keywords

• nonn
• tabl

Comments

Row sums are A384274.

Examples

			Table begins:
 n\k|  0    1     2     3    4   5  6  7
----+------------------------------------
  0 |  1;
  1 |  1,   1;
  2 |  1,   1,    0;
  3 |  1,   3,    1,    0;
  4 |  3,   8,    8,    1,   0;
  5 |  7,  31,   43,   14,   1,  0;
  6 | 24, 126,  261,  152,  18,  0, 0;
  7 | 88, 598, 1543, 1467, 369, 14, 0, 0;
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 0..119
• Wikipedia, Quarter cubic honeycomb
• Peter Kagey, Illustration of row 4.

Crossrefs

Cf. A038169, A384274.

Cf. A365970 (tetrahedral-octahedral honeycomb).

Formula

T(n,0) = A038169(n).

Extensions

More terms from Bert Dobbelaere, Jun 12 2025