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.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
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},
     publisher = {mathdoc},
     volume = {10},
     number = {8},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_8_a6/}
}
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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/