%I A154642
%S A154642 1,6,77,732,7278,71634,707076
%N A154642 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 (a)" to count them (see the reference), 
               to the sum of the squares of the bends of the initial five mutually 
               tangent spheres.
%C A154642 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.
%D A154642 C. L. Mallows, Growing Apollonian packings. J. Integer Sequences 12, 
               article 09.2.1 (2009)
%e A154642 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 A154642 For other sequences relating to the 3-dimensional case, see A154638-A154645.
%Y A154642 Sequence in context: A009763 A028979 A082629 this_sequence A154645 A030641 
               A116280
%Y A154642 Adjacent sequences: A154639 A154640 A154641 this_sequence A154643 A154644 
               A154645
%K A154642 hard,more,nonn
%O A154642 0,2
%A A154642 Colin Mallows (colinm(AT)research.avayalabs.com), Jan 13 2009