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A343909 Number of generalized polyforms on the tetrahedral-octahedral honeycomb with n cells. 3
1, 2, 1, 4, 9, 44, 195, 1186, 7385, 49444, 337504 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
This sequence counts "free" polyforms where holes are allowed. This means that two polyforms are considered the same if one is a rigid transformation (translation, rotation, reflection, or a combination thereof) of the other.
LINKS
EXAMPLE
For n = 1, the a(1) = 2 polyforms are the tetrahedron and the octahedron.
For n = 2, the a(2) = 1 polyform is a tetrahedron and an octahedron connected at a face.
For n = 3, there are a(3) = 4 polyforms with 3 cells:
- 3 consisting of one octahedron with two tetrahedra, and
- 1 consisting of two octahedra and one tetrahedron.
For n = 4, there are a(4) = 9 polyforms with 4 cells:
- 3 with one octahedron and three tetrahedra,
- 5 with two octahedra and three octahedra, and
- 1 with three octahedra and one tetrahedron.
For n = 5, there are a(5) = 44 polyforms with 5 cells:
- 6 with one octahedron and four tetrahedra,
- 24 with two octahedra and three tetrahedra,
- 13 with three octahedra and two tetrahedra, and
- 1 with four octahedra and one tetrahedron.
CROSSREFS
Analogous for other honeycombs/tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A038119 (cubical), A068870 (tesseractic), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).
Sequence in context: A343398 A097949 A268572 * A117338 A279927 A137634
KEYWORD
nonn,hard,more
AUTHOR
Drake Thomas and Peter Kagey, May 03 2021
STATUS
approved

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Last modified April 19 16:52 EDT 2024. Contains 371794 sequences. (Running on oeis4.)