Geodesic
On Sequences \(G_n\) satisfying \(G_n=(d+2)G_{n-1} - G_{n-2}\)
Journal of integer sequences, Tome 10 (2007) no. 8
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.
Keywords: skinny trees, outdegree, tilings, Fibonacci numbers, lattice paths 
@article{JIS_2007__10_8_a6,
     author = {Chen,  Ricky X.F. and Shapiro,  Louis W.},
     title = {On {Sequences} {\(G_n\)} satisfying {\(G_n=(d+2)G_{n-1}} - {G_{n-2}\)}},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {8},
     zbl = {1141.05305},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_8_a6/}
}
TY  - JOUR
AU  - Chen,  Ricky X.F.
AU  - Shapiro,  Louis W.
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JO  - Journal of integer sequences
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Chen,  Ricky X.F.; Shapiro,  Louis W. On Sequences \(G_n\) satisfying \(G_n=(d+2)G_{n-1} - G_{n-2}\). Journal of integer sequences, Tome 10 (2007) no. 8. http://geodesic.mathdoc.fr/item/JIS_2007__10_8_a6/