GENERATING INFINITELY MANY PERFECT SQUARES AMONG NARAYANA NUMBERS

The Narayana numbers [endif]--> form a triangular array of positive integers, introduced in 1915-1916 by the combinatorialist P. A. MacMahon, and rediscovered in 1955 by the statistician T. V. Narayana. Among Narayana numbers, it turns out that N (1728,28) is a perfect square. A natural question that would arise is whether there exist other values of a such that [endif]-->forms a perfect square? In this paper, we discuss ways of determining infinitely many values of a, for given choice of[endif]-->, such that the Narayana numbers [endif]-->forms a perfect square