

A154643


a(n) is the number of spheres that are added in the nth generation of Apollonian packing of threedimensional spheres, starting with five mutually tangent spheres and using "strategy (b)" to count them (see the reference).


0




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 3dimensional case, see A154638A154645.
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



