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.

A154641 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 (a)" to count them (see the reference), to the sum of the bends of the initial five mutually tangent spheres.

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%I A154641 #6 Aug 18 2017 16:01:52
%S A154641 1,3,20,108,630,3570,20460
%N A154641 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 (a)" to count them (see the reference), to the sum of the bends of the initial five mutually tangent spheres.
%C A154641 In strategy (a) we do not count spheres that can be obtained (by reflection) from the "extra" quintuples of spheres that appear in the previous generation.
%H A154641 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 A154641 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 A154641 For other sequences relating to the 3-dimensional case, see A154638-A154645.
%K A154641 hard,more,nonn
%O A154641 0,2
%A A154641 _Colin Mallows_, Jan 13 2009