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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). 0
5, 5, 20, 90, 330, 1290 (list; graph; refs; listen; history; text; internal format)



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


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

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


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.


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




Colin Mallows, Jan 13 2009



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Last modified November 28 08:48 EST 2022. Contains 358407 sequences. (Running on oeis4.)