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

[N. J. A. Sloane]

> 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?

This is indeed one of the standard ways to define the Bell numbers, A000110.

That entry gives many more details.

Also many references (the Comtet book is especially nice)


 Best regards
 			 Neil