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A154635 Ratio of the sum of the bends of the 5-dimensional spheres added in the n-th generation of Apollonian packing to the sum of the bends of the initial configuration of seven mutually tangent spheres. 2
1, 2, 15, 108, 774, 5544, 39708, 284400, 2036952, 14589216, 104492016, 748400832, 5360254560, 38391631488, 274971524544, 1969422407424, 14105550112128, 101027866452480, 723589630947072, 5182549848861696, 37118861005211136, 265855588948518912 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Colin Mallows, Growing Apollonian packings, J. Integer Sequences v.12, article 09.2.1 (2009).

Index entries for linear recurrences with constant coefficients, signature (8,-6).

FORMULA

G.f. (1-x)*(1-5*x) / (1-8*x+6*x^2).

From Colin Barker, Nov 16 2016: (Start)

a(n) = (((4-sqrt(10))^n*(-8+sqrt(10))+(4+sqrt(10))^n*(8+sqrt(10))))/(12*sqrt(10)) for n>0.

a(n) = 8*a(n-1) - 6*a(n-2) for n>2.

(End)

EXAMPLE

Starting with seven 5-dimensional spheres with bends 0,0,1,1,1,1,1 summing to 5, the first derived generation has seven spheres, with bends 1,1,1,1,1,5/2,5/2 summing to 10. So a(1) = 10/5 = 2.

MATHEMATICA

CoefficientList[Series[(1 - z) (1 - 5 z)/(1 - 8 z + 6 z^2), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

PROG

(PARI) Vec((1-x)*(1-5*x)/(1-8*x+6*x^2) + O(x^30)) \\ Colin Barker, Nov 16 2016

CROSSREFS

Cf. A135849 for dim=2. A137146 for the sum of squares of bends when dim=2. A154636 and A154637 for starting with three spheres in 2 dimensions. A154638-A154645 for results in the three-dimensional case.

Sequence in context: A279087 A037740 A037635 * A062808 A162773 A140637

Adjacent sequences:  A154632 A154633 A154634 * A154636 A154637 A154638

KEYWORD

easy,nonn

AUTHOR

Colin Mallows, Jan 13 2009

STATUS

approved

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)