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.

1, 6, 77, 1278, 15978, 216366

Offset: 0

Author

Colin Mallows, Jan 13 2009

Keywords

• hard
• more
• nonn

Comments

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

Examples

			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.
		

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.