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
KEYWORD
easy,nonn
AUTHOR
Colin Mallows, Jan 13 2009
STATUS
approved