Type: Article

On sums of distinct odd squares arising from a class of totally symmetric plane partitions

Blecher, A.; Knopfmacher, A.; Luca, F;

Abstract:

We prove some results about the coefficients r(n) of Pi(i >= 0)(1 + q(3i2+3i+1)). These coefficients count the number of a special type of partitions of n, namely totally symmetric plane partitions with self conjugate main diagonal. In particular, we prove the conjecture that n = 860 is the largest n such that r(n) = 0.