|
Search: id:A154643
|
|
|
| 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
1
|
| |
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation.
|
|
REFERENCES
|
C. L. Mallows, Growing Apollonian packings. J. Integer Sequences 12, article 09.2.1 (2009)
|
|
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 this_sequence A127513 A091260 A171219
Adjacent sequences: A154640 A154641 A154642 this_sequence A154644 A154645 A154646
|
|
KEYWORD
|
hard,more,nonn
|
|
AUTHOR
|
Colin Mallows (colinm(AT)research.avayalabs.com), Jan 13 2009
|
|
|
Search completed in 0.002 seconds
|
