# Good $$n$$-gons

Consider a convex $$2015$$-gon $$P$$. An $$n$$-gon with all its vertices among those of $$P$$ is called good if it doesn't share any edge in common with $$P$$. Let the number of such $$n$$-gons be $$N_n$$.

Find the digit sum of $$N_{20}+N_{15}$$.

Note 1 : All numbers are expressed in base $$10$$. You may need a CAS to find the digit sum.

Note 2 : Try this easier variant first.

Looking forward to see different solutions :)

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