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A045506 Inscribe 2 spheres of curvature 2 inside sphere of curvature -1, continue to inscribe spheres where possible; sequence gives list of curvatures. 4
-1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A 3-dimensional Apollonian (or Soddy) problem.

Appears to be congruent to 0 or 2 mod 3.

LINKS

Table of n, a(n) for n=0..69.

FORMULA

Appears to coincide with a(n)=2+3*floor((n-1)/2)+(1+(-1)^n)/2-0^n, in which case the g.f. is (-1+3x+2x^2-x^3)/((1+x)(1-x)^2). - Paul Barry, Sep 11 2008

MATHEMATICA

CoefficientList[Series[(-z^3 + 2 z^2 + 3 z - 1)/((z - 1)^2 (z + 1)), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

CROSSREFS

Cf. A042944.

Sequence in context: A195123 A248758 A267528 * A007494 A258575 A052490

Adjacent sequences:  A045503 A045504 A045505 * A045507 A045508 A045509

KEYWORD

sign,nice

AUTHOR

Brian Galebach

STATUS

approved

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Last modified October 22 02:06 EDT 2017. Contains 293756 sequences.