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\centerline{ \bf Riccati meets Fibonacci}\psn
\centerline{Wolfdieter L a n g}\psn 
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The generating functions for generalized {\sl Fibonacci} and {\sl Lucas} 
numbers are shown to be the unique solutions to {\sl Riccati} equations 
with certain initial conditions. This observation leads directly to recursion 
relations for $k$-fold convolutions of these numbers which have been partly 
found earlier in a different way. 
A generalization of this method to so called $p-${\sl Fibonacci} numbers is 
also considered.     
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