This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A154643 #6 Aug 18 2017 16:07:26 %S A154643 5,5,20,90,330,1290 %N 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). %C A154643 In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation. %H A154643 C. L. Mallows, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Mallows/mallows8.html">Growing Apollonian Packings</a>, J. Integer Sequences, 12 (2009), article 09.2.1. %e A154643 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. %Y A154643 For other sequences relating to the 3-dimensional case, see A154638-A154645. %K A154643 hard,more,nonn %O A154643 0,1 %A A154643 _Colin Mallows_, Jan 13 2009