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

0,1

Comments

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

Links

Table of n, a(n) for n=0..6.

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

Example

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).

Crossrefs

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

Sequence in context: A205882 A099921 A139470 * A154643 A186411 A255452

Adjacent sequences: A154637 A154638 A154639 * A154641 A154642 A154643

Keyword

hard,more,nonn

Author

Colin Mallows, Jan 13 2009

Status

approved