Summary: In this note, we study a class of sequences $G_{n}$ satisfying $G_{n} = (d+2)G_{n-1} - G_{n-2}$. Note that the Fibonacci numbers $G_{n} = F_{2n}, n >1$ and $G_{n} = F_{2n+1}, n > 0$ occur when $d=1$ with suitable initial conditions. We present a general interpretation for this class of sequences in terms of ordered trees which we count by nodes and outdegrees. Further more, several other related integer sequences are also studied.

skinny trees, outdegree, tilings, Fibonacci numbers, lattice paths