Local Maxima of Number of Goldbach Decompositions

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Let $\mathbb E$ be the set of even positive integers.

Let $G: \mathbb E \to \N$ be the mapping defined as:

$\forall n \in \mathbb E: \map G n =$ the number of Goldbach decompositions of $n$.

Then $G$ has local maxima when $n$ is a multiple of $6$.


Historical Note

This theorem is reported by David Wells, in his $1997$ Curious and Interesting Numbers, 2nd ed. to have been demonstrated by R.M. Sternheimer, in Volume $24$ of Journal of Recreational Mathematics, page $30$, but corroborative evidence is not easily come by.