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A154643 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 (b)" to count them (see the reference).

Original entry on oeis.org

5, 5, 20, 90, 330, 1290
Offset: 0

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Author

Colin Mallows, Jan 13 2009

Keywords

Comments

In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation.

Examples

			For a(3), we apply reflection to the 20 quintuples that were generated in the second generation and also to the 10 "extra" quintuples which appear at this stage, each consisting of two spheres in the initial configuration and three from generation 2. These quintuples will appear as ABA = BAB in the third generation.

Links

Crossrefs

For other sequences relating to the 3-dimensional case, see A154638-A154645.
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