ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

Blecher ['Geometry for totally symmetric plane partitions (TSPPs) with self-conjugate main diagonal', Util. Math. 88 (2012), 223-235] defined the combinatorial objects known as 1-shell totally symmetric plane partitions of weight n. He also proved that the generating function for f (n); the number of 1-shell totally symmetric plane partitions of weight n, is given by Sigma f (n)q(n) = 1 + Sigma q(3n-2) Pi (1 + q(6i+3)) n >= 0 n >= 1 i=0 In this brief note, we prove a number of arithmetic properties satisfied by f (n) using elementary generating function manipulations and well-known results of Ramanujan and Watson.