A154644 a(n) is the ratio of the sum 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 bends of the initial five mutually tangent spheres.

1, 3, 20, 174, 1170, 8454

Offset

0,2

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

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.

Crossrefs

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

Sequence in context: A357094 A216583 A354018 * A321276 A000891 A242164

Adjacent sequences: A154641 A154642 A154643 * A154645 A154646 A154647

Keyword

hard,more,nonn

Author

Colin Mallows, Jan 13 2009

Status

approved