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 :)

Image credit: Wikipedia David Eppstein

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