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Search: id:A154639
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| A154639 |
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a(n) is the number of reduced words of length n (i.e. all possible length-reducing cancellations have been applied) in the generators of the "Apollonian reflection group" in three dimensions. This is a Coxeter group with five generators, satisfying the identities (S_i)^2 = (S_i S_j)^3 = I. |
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+0
1
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OFFSET
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0,2
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COMMENT
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ABA and BAB are equal, but are counted as distinct reduced words.
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REFERENCES
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R. L. Graham, J. C. Lagarias, C. L. Mallows, A. R. Wilks and C. Yan, Apollonian circle Packings: Geometry and Group Theory III Higher Dimensions. Discrete and Computational Geometry 35: 37-72 (2006).
C. L. Mallows, Growing Apollonian packings. J. Integer Sequences 12, article 09.2.1 (2009)
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EXAMPLE
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All 80 square-free words of length 3 are counted, so a(3) = 80.
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CROSSREFS
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For other sequences relating to the 3-dimensional case, see A154638-A154645.
Sequence in context: A028814 A079820 A117422 this_sequence A003947 A033131 A022021
Adjacent sequences: A154636 A154637 A154638 this_sequence A154640 A154641 A154642
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KEYWORD
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more,nonn
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AUTHOR
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Colin Mallows (colinm(AT)research.avayalabs.com), Jan 13 2009
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