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Number of linear connected animals formed from n 6-gon connected truncated octahedra.
+10
3
1, 1, 3, 7, 29, 114, 578, 2890, 15431, 82091, 442702, 2377819, 12820705
COMMENTS
Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for rhombic dodecahedra is A363209.
Number of linear connected animals formed from n rhombic dodecahedra.
+10
3
1, 1, 3, 10, 52, 288, 1826, 11702, 76586, 501429, 3289245, 21554198
COMMENTS
Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for truncated octahedra is A363208.
Number of linear connected animals formed from n 4-gon or 6-gon connected truncated octahedra.
+10
3
1, 2, 5, 19, 95, 598, 4190, 30809, 230104, 1728305, 12993821
COMMENTS
Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for truncated octahedra is A363209. The analog for rhombic dodecahedra is A363208.
Number of simple chains with n-1 edges strongly embedded in a simple cubic lattice.
+10
2
1, 3, 15, 63, 267, 1107, 4623, 19071, 78987, 324543, 1337511, 5483235, 22527315, 92200455, 377965479, 1544925891, 6322891707
COMMENTS
Gaunt et al. also enumerate clusters with upper limits on the vertex degree.
a(n) is the number of fixed linear or snake polycubes of size n. - John Mason, Sep 27 2024
Number of free linear polycubes of size n, identifying rotations but not reflections.
+10
2
1, 1, 2, 5, 16, 54, 212, 827, 3369, 13653, 56052, 229004, 939935, 3843859, 15753903, 64380796, 263475472, 1075780425, 4397161320, 17939394036, 73251877235, 298646347226, 1218453344740
COMMENTS
Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.
Additionally identifying reflections gives A363202.
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