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).

5, 5, 20, 90, 330, 1290

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..5.

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

Example

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.

Crossrefs

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

Sequence in context: A099921 A139470 A154640 * A186411 A255452 A255446

Adjacent sequences: A154640 A154641 A154642 * A154644 A154645 A154646

Keyword

hard,more,nonn

Author

Colin Mallows, Jan 13 2009

Status

approved