Nice polynomial

Author: mathforces
Problem has been solved: 7 times

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In how many ways from the set of pairs of numbers $(a, b)$ such that $a, b \in \{0,1,2,3 \}$ one can choose a subset $S$ such that there exist positive coefficients $c_ {i,\ j}$ for $(i,\ j) \in S$ such that the polynomial $$f(x,y) = \sum_{(i,\ j) \in S} c_ {i,\ j} x^i y^ j$$ is bounded below?