Magic Numbers and the Island of Stability

Nuclei have a shell structure just as for electrons surrounding an atom. The shell structure in a nucleus is more complicated than for electrons. Nuclei with full shells are more stable than other nuclei, as shown by the fact that nuclei at the end of decay chains are more stable, and have a number of protons plus neutrons equal to a 'magic number'. The first few magic numbers are
2, 8, 14, 20, 32, 50, 126
The nth magic number is equal to  
\[2({}^n C_1 + {}^n C_2 + ....+ {}^n C_n)\]
It is believed that this rule does not hold for higher magic numbers because the shape of the nucleus is believed to change for higher numbers than above.
There are forecast to be stable nuclei in an island of stability with 298, 318 and 360 nucleons.