This is just A000081, right? --Michael On Mon, Apr 26, 2010 at 3:27 PM, Dan Asimov <dasimov@earthlink.net> wrote:

Define an n-bloop to be any set of any n disjoint geometric circles (of possibly unequal radii) in the plane.

If B is an n-bloop, then by continuously varying the centers and radii of its circles C_k we can get a family {B_t | 0 <= t <= 1} of n-bloops with B_0 = B . . . that is, AS LONG AS at no time t do any two of the n circles of B_t intersect.

If B = B(0) can be so varied to B' = B(1), we say B and B' are *equivalent*.

Let f(n) be the number of equivalence classes of n-bloops.

What is an expression for f(n) in closed form?

(I just thought of this problem and have a quick guess, but don't know the answer at the moment.)

--Dan

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