Geodesic
Some formulas for numbers of restricted words
Journal of integer sequences, Tome 20 (2017) no. 6
For an arithmetic function $f_{0}$, we consider the number $c_{m}(n,k)$ of weighted compositions of $n$ into $k$ parts, where the weights are the values of the $(m-1)^{th}$ invert transform of $f_{0}$. We connect $c_{m}(n,k)$ with $c_{1}(n,k)$ via Pascal matrices. We then relate $c_{m}(n,k)$ to the number of certain restricted words over a finite alphabet. In addition, we develop a method which transfers some properties of restricted words over a finite alphabet to words over a larger alphabet.
Classification : 05A10, 11B39
Keywords: binary word, integer composition, restricted word, Pascal matrix 
@article{JIS_2017__20_6_a3,
     author = {Janji\'c,  Milan},
     title = {Some formulas for numbers of restricted words},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {6},
     zbl = {1365.05012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a3/}
}
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Janjić,  Milan. Some formulas for numbers of restricted words. Journal of integer sequences, Tome 20 (2017) no. 6. http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a3/