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A007173
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Number of simplicial 3-clusters with n cells.
(Formerly M3401)
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1
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1, 1, 1, 4, 10, 40, 171, 831, 4147, 21822, 117062, 642600, 3582322, 20256886, 115888201, 669911568, 3907720521, 22979343010, 136107859377, 811430160282
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also arises in enumeration of stereo isomers of alkane systems.
A simplicial d-cluster may be informally described as being constructed by gluing regular d-simplexes together facet-by-facet, at each stage gluing a new simplex to exactly one facet of a cluster already constructed. The equivalence classes of such clusters under rigid motions are in one-to-one correspondence with the combinatorial types of stack polytopes. [Jonathan Vos Post, Apr 22, 2011]
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REFERENCES
| S. J. Cyvin et al., Enumeration of staggered conformers of alkanes: complete solution ..., J. Molec. Struct., 413 (1997), 237-239.
F. Hering et al., The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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CROSSREFS
| Sequence in context: A149210 A149211 A149212 * A114918 A149213 A149214
Adjacent sequences: A007170 A007171 A007172 * A007174 A007175 A007176
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KEYWORD
| nonn,nice,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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