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

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.