[seqfan] Inequivalent ways C_n of coloring a strip of n+1 boxes (...)

[Gottfried Helms]

Dear Seqfans -

 I got a request which I cannot handle myself. Has this been
 discussed before or can it be solved by reasonable means? I'd
 like to forward any helpful answer to the correspondent.

 TIA -

Gottfried Helms


Forwarded message:
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I am a PhD student in Statistical Physics in SISSA and I am studying
percolation theory. I was looking at the problem of finding the number
of inequivalent  ways C_n of coloring a strip of n+1 boxes in such way
that  adjacent boxes always have different colors.
Numerically I obtained the sequence

C_1=1; C_2=1; C_3=2; C_4=5; C_5=15, up to C_10=115975.

These are Bells number and on Wikipedia article I found your notes.
However it seems that this connection it is not very well known and I
have no idea to who ask about it.
Would you be so kind to tell me if there is a proof that the number of
inequivalent ways of coloring a strip of n+1 boxes in such way that no
adjacent boxes have the same colour is a Bell number?
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