cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A384754 The number of face-connected components of polyhedra in the omnitruncated cubic honeycomb up to translation, rotation, and reflection.

Original entry on oeis.org

1, 2, 4, 22, 179, 2227, 34278, 591787, 10765367, 201844314, 3860318208
Offset: 0

Views

Author

Peter Kagey, Jun 09 2025

Keywords

Comments

The omnitruncated cubic honeycomb consists of truncated cuboctahedra and octagonal prisms.

Crossrefs

Cf. A384755.
Cf. A038119 (cubic honeycomb), A038181 (bitruncated cubic honeycomb), A343909 (tetrahedral-octahedral honeycomb), A384254 (rectified cubic honeycomb), A384274 (quarter cubic honeycomb).

Extensions

a(7)-a(10) from Bert Dobbelaere, Jun 14 2025

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.

Original entry on oeis.org

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

Views

Author

Peter Kagey, Jun 09 2025

Keywords

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;
		

Crossrefs

Cf. A384755 (rotation and reflection).

Formula

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

Extensions

More terms from Bert Dobbelaere, Jun 14 2025

A384782 Triangle read by rows: T(n,k) is the number of face-connected polyhedral components consisting of k cuboctahedra and n-k octahedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb, 0<=k<=n.

Original entry on oeis.org

1, 1, 1, 0, 1, 1, 0, 3, 4, 2, 0, 3, 18, 12, 7, 0, 6, 60, 126, 75, 23, 0, 3, 165, 751, 1025, 473, 112, 0, 3, 346, 3784, 9414, 8936, 3539, 607, 0, 1, 565, 14112, 66503, 108739, 80531, 27027, 3811, 0, 1, 723, 42420, 362939, 994542, 1204093, 725795, 212122, 25413, 0, 0, 723, 101237, 1586479, 7065791, 13389295, 12792264, 6512671, 1678783, 178083
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 09 2025

Keywords

Comments

Also the number of face-connected polyhedral components consisting of k truncated cubes and n-k octahedra in the truncated cubic honeycomb up to translation, rotation, and reflection of the honeycomb.
Row sums are given by A384254.

Examples

			Table begins:
   0 | 1;
   1 | 1, 1;
   2 | 0, 1,   1;
   3 | 0, 3,   4,     2;
   4 | 0, 3,  18,    12,      7;
   5 | 0, 6,  60,   126,     75,     23;
   6 | 0, 3, 165,   751,   1025,    473,     112;
   7 | 0, 3, 346,  3784,   9414,   8936,    3539,    607;
   8 | 0, 1, 565, 14112,  66503, 108739,   80531,  27027,   3811;
   9 | 0, 1, 723, 42420, 362939, 994542, 1204093, 725795, 212122, 25413;
		

Crossrefs

Cf. A384254.
Cf. A365970 (tetrahedral-octahedral honeycomb), A384486 (quarter cubic honeycomb), A384755 (omnitruncated cubic honeycomb).

Formula

T(n,n) = A038119(n).
Showing 1-3 of 3 results.