Identities involving Narayana numbers

2018/05/06 by Cerda-Morales, Gamaliel
#11B37 #11B83 #15A36 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.02255

Abstract

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 (r≥3) with initial condition N₀ =0, N₁ = N₂= 1. In this paper, the ar+b subscripted Narayana numbers will be expressed by three a step apart Narayana numbers for any 1≤ b≤ a (a∈ ℤ). Furthermore, we study the sum S_N,r^(4,b)=∑_k=0^rN_4k+b of 4 step apart Narayana numbers for any 1≤ b≤ 4.

Related

• Narayana's cows numbers which are concatenations of three repdigits in base ρ
• Members of Narayana's cow sequence that are concatenations of two repdigits
• Narayana numbers that are products of two Fibonacci numbers
• Repdigits in Narayana's Cows Sequence and their Consequences
• k-Fibonacci numbers which are Narayana's cows numbers