Geodesic
Sequences that satisfy \(a(n-a(n))=0\)
Journal of integer sequences, Tome 8 (2005) no. 5
We explore the properties of some sequences for which $a(n-a(n))=0$. Under the natural restriction that $a(n) n$ the number of such sequences is a Bell number. Adding other natural restrictions yields sequences counted by the Catalan numbers, the Narayana numbers, the triangle of triangular binomial coefficients, and the Schröder numbers.
Keywords: Bell number, Catalan number, schr$\ddot $oder number, bijection 
@article{JIS_2005__8_5_a5,
     author = {Kube,  Nate and Ruskey,  Frank},
     title = {Sequences that satisfy \(a(n-a(n))=0\)},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {5},
     zbl = {1106.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a5/}
}
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Kube,  Nate; Ruskey,  Frank. Sequences that satisfy \(a(n-a(n))=0\). Journal of integer sequences, Tome 8 (2005) no. 5. http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a5/