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A154645
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 (b)" to count them (see the reference), to the sum of the squares of the bends of the initial five mutually tangent spheres.
12
1, 6, 77, 1278, 15978, 216366
OFFSET
0,2
COMMENTS
In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation.
LINKS
C. L. Mallows, Growing Apollonian Packings, J. Integer Sequences, 12 (2009), article 09.2.1.
EXAMPLE
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.
CROSSREFS
For other sequences relating to the 3-dimensional case, see A154638-A154645.
Sequence in context: A154642 A282783 A215551 * A299434 A355764 A301834
KEYWORD
hard,more,nonn
AUTHOR
Colin Mallows, Jan 13 2009
STATUS
approved