The generalized order-$k$ Narayana's cows numbers

Year, pages: 2016, 795 - 802

Narayana's cows problem is a problem similar to the Fibonacci's rabbit problem. We define the numbers which are the solutions of this problem as Narayana's cows numbers. Narayana's cows sequence satisfies the third order recurrence relation $N_r=N_r-1+N_r-3$ with initial condition $N₀=N₁=N₂=1$. In this paper, we define a new recurrence which is called generalized order-$k$ Narayana's cows sequence and by using this generalization and some matrix properties, we give some identities related to the Narayana's cows numbers.

Bilgici, G. 2016. The generalized order-$k$ Narayana's cows numbers. In Mathematica Slovaca, vol. 66, no.4, pp. 795-802. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0181

Bilgici, G. (2016). The generalized order-$k$ Narayana's cows numbers. Mathematica Slovaca, 66(4), 795-802. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0181