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Search: id:A154642
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| A154642 |
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a(n) is the ratio of the sum of the squares of the bends of the spheres that are added in the n-th generation of Apollonian packing of three-dimensional spheres, using "strategy (a)" to count them (see the reference), to the sum of the squares of the bends of the initial five mutually tangent spheres. |
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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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In strategy (a) we do not count spheres that can be obtained (by reflection) from the "extra" quintuples of spheres that appear 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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Starting with five spheres with bends 0,0,1,1,1, the first derived generation has 5 spheres with bends 1,1,1,3,3, so a(2) = 9/3 = 3.
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CROSSREFS
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For other sequences relating to the 3-dimensional case, see A154638-A154645.
Sequence in context: A009763 A028979 A082629 this_sequence A154645 A030641 A116280
Adjacent sequences: A154639 A154640 A154641 this_sequence A154643 A154644 A154645
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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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