This paper presents a construction for symmetric, non-negative polynomials, which are not sums of squares. It explicitly generalizes the Motzkin polynomial and the Robinson polynomials to families of non-negative polynomials, which are not sums of squares. The degrees of the resulting polynomials can be chosen in advance.

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CWI
CWI. Probability, Networks and Algorithms [PNA]
Networks and Optimization

Bosse, H. (2007). Symmetric, positive polynomials, which are not sums of squares. CWI. Probability, Networks and Algorithms [PNA]. CWI.