Narayana’s cows sequence and its companion, the Tridovan sequence

Abstract

We show that there is a fundamental identity connecting Narayana’s numbers and Tridovan numbers. This identity expresses Narayana’s number as the sum of two Tridovan numbers ($N_n=T_n+T_{n-1}$), thereby enabling the quick derivation of Narayana–Tridovan summation formulas.