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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. 2

%I

%S 1,3,20,174,1170,8454

%N 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 In strategy (b) we count all spheres that can be generated (by reflection) from all quintuples that appeared in the previous generation.

%H 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 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 For other sequences relating to the 3-dimensional case, see A154638-A154645.

%K hard,more,nonn

%O 0,2

%A _Colin Mallows_, Jan 13 2009

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Last modified November 27 21:40 EST 2022. Contains 358406 sequences. (Running on oeis4.)