A. Blecher, A. Knopfmacher, F. Luca and S. Wagner: On sums of distinct odd squares arising from a class of totally symmetric plane partitions, p.163-171


We prove some results about the coefficients $r_n$ of $\prod_{i\ge 0} (1+q^{3i^2+3i+1})$. 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 $r_n=0$.

Key Words: Partitions, representations as sums of squares.

2000 Mathematics Subject Classification: Primary: 05A15;
Secondary: 05A16.

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