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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. 12
1, 6, 77, 1278, 15978, 216366 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..5.

C. L. Mallows, Growing Apollonian Packings, J. Integer Sequences, 12 (2009), article 09.2.1.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A154642 A282783 A215551 * A299434 A355764 A301834

Adjacent sequences:  A154642 A154643 A154644 * A154646 A154647 A154648

KEYWORD

hard,more,nonn

AUTHOR

Colin Mallows, Jan 13 2009

STATUS

approved

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Last modified October 3 02:59 EDT 2022. Contains 357230 sequences. (Running on oeis4.)