A154640 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).

5, 5, 20, 60, 210, 690, 3330

Offset: 0

Author

Colin Mallows, Jan 13 2009

Keywords

• hard
• more
• nonn

Comments

In strategy (a) we do not count spheres that are generated (by reflection) from quintuples that were not generated in the previous generation.

Examples

			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).
		

Links

• C. L. Mallows, Growing Apollonian Packings, J. Integer Sequences, 12 (2009), article 09.2.1.

Crossrefs

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