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 A154644 #6 Aug 18 2017 16:05:47 %S A154644 1,3,20,174,1170,8454 %N 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. %C A154644 In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation. %H A154644 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 A154644 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. %Y A154644 For other sequences relating to the 3-dimensional case, see A154638-A154645. %K A154644 hard,more,nonn %O A154644 0,2 %A A154644 _Colin Mallows_, Jan 13 2009