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I think the number of maximal sets of non-intersecting diagonals for 11-gon is 29, or F(11) = 29 .
By inspection we obtain following data: F(5) = 1, F(6) = 3, F(7) = 4, F(8) = 7. According to these data we have to do with a Fibonacci-like sequence, F(n) = F(n-1) + F(n-2). So, if we extrapolate the obtained data we can write: