cp's OEIS Frontend

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.

A154645 a(n) is the ratio of the sum of the squares 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 squares of the bends of the initial five mutually tangent spheres.

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%I A154645 #6 Aug 18 2017 15:55:03
%S A154645 1,6,77,1278,15978,216366
%N A154645 a(n) is the ratio of the sum of the squares 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 squares of the bends of the initial five mutually tangent spheres.
%C A154645 In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation.
%H A154645 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 A154645 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 A154645 For other sequences relating to the 3-dimensional case, see A154638-A154645.
%K A154645 hard,more,nonn
%O A154645 0,2
%A A154645 _Colin Mallows_, Jan 13 2009