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.

1, 1, 1, 1, 2, 1, 3, 7, 10, 2, 12, 41, 76, 46, 4, 61, 335, 809, 777, 232, 13, 407, 3065, 9512, 12863, 7186, 1206, 39, 3226, 30401, 114516, 204143, 172377, 60421, 6548, 155, 28335, 311782, 1381363, 3054599, 3507278, 1975767, 469525, 36081, 637, 262091, 3260971, 16569719, 43731912

Offset

0,5

Comments

Row sums are A384754.

Links

Bert Dobbelaere, Table of n, a(n) for n = 0..65

Peter Kagey, Illustration of row 3.

Wikipedia, Convex uniform honeycomb

Formula

T(n,0) = A038171(n).

Example

0 |   1;
1 |   1,    1;
2 |   1,    2,    1;
3 |   3,    7,   10,     2;
4 |  12,   41,   76,    46,    4;
5 |  61,  335,  809,   777,  232,   13;
6 | 407, 3065, 9512, 12863, 7186, 1206, 39;

Crossrefs

Cf. A038171, A384754, A384756.

Cf. A365970 (tetrahedral-octahedral honeycomb), A384486 (quarter cubic honeycomb), A384782 (rectified cubic honeycomb).

Sequence in context: A178079 A258987 A174254 * A024404 A077173 A063509

Adjacent sequences: A384752 A384753 A384754 * A384756 A384757 A384758

Keyword

nonn,tabl

Author

Peter Kagey, Jun 09 2025

Extensions

More terms from Bert Dobbelaere, Jun 14 2025

Status

approved