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.

1, 2, 15, 108, 774, 5544, 39708, 284400, 2036952, 14589216, 104492016, 748400832, 5360254560, 38391631488, 274971524544, 1969422407424, 14105550112128, 101027866452480, 723589630947072, 5182549848861696, 37118861005211136, 265855588948518912

Offset: 0

Author

Colin Mallows, Jan 13 2009

Keywords

• easy
• nonn

Examples

			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.
		

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).

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.

Programs

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 *)

PARI

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

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)