Geodesic
A simplified Binet formula for \(k\)-generalized Fibonacci numbers
Journal of integer sequences, Tome 17 (2014) no. 4
In this paper, we present a Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc.). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula in order to generate the desired sequence.
Classification : 11B39, 11C08, 33F05, 65D20
Keywords: k-generalized Fibonacci numbers, binet form, tribonacci number, tetranacci number, pentanacci number 
@article{JIS_2014__17_4_a1,
     author = {Dresden,  Gregory P.B. and Du,  Zhaohui},
     title = {A simplified {Binet} formula for \(k\)-generalized {Fibonacci} numbers},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {4},
     zbl = {1360.11031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a1/}
}
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Dresden,  Gregory P.B.; Du,  Zhaohui. A simplified Binet formula for \(k\)-generalized Fibonacci numbers. Journal of integer sequences, Tome 17 (2014) no. 4. http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a1/