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Search: id:A154640
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| A154640 |
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a(n) is the number of spheres that are added in the n-th generation of Apollonian packing of three-dimensional spheres, starting with five mutually tangent spheres and using "strategy (a)" to count them (see the reference). |
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+0
2
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OFFSET
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0,1
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COMMENT
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In strategy (a) we do not count spheres that are generated (by reflection) from quintuples that were not generated in the previous generation.
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REFERENCES
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C. L. Mallows, Growing Apollonian packings. J. Integer Sequences 12, article 09.2.1 (2009)
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EXAMPLE
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For a(3), we apply reflection only to the 20 quintuples that were generated in the second generation, ignoring the 10 "extra" quintuples (which will appear as ABA = BAB in the third generation).
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CROSSREFS
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For other sequences relating to the 3-dimensional case, see A154638-A154645.
Sequence in context: A094338 A099921 A139470 this_sequence A154643 A127513 A091260
Adjacent sequences: A154637 A154638 A154639 this_sequence A154641 A154642 A154643
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KEYWORD
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hard,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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