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 ∑ _n≥0 f(n)qⁿ = 1+ ∑_n≥1q^3n-2 ∏_i=0^n-2(1+q⁶ⁱ⁺³). 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.