%I A154645
%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.
%D A154645 C. L. Mallows, Growing Apollonian packings. J. Integer Sequences 12, 
               article 09.2.1 (2009)
%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.
%Y A154645 Sequence in context: A028979 A082629 A154642 this_sequence A030641 A116280 
               A134788
%Y A154645 Adjacent sequences: A154642 A154643 A154644 this_sequence A154646 A154647 
               A154648
%K A154645 hard,more,nonn
%O A154645 0,2
%A A154645 Colin Mallows (colinm(AT)research.avayalabs.com), Jan 13 2009