You apparently misunderstood the example.
If you have two coils with perfect coupling, the total inductance (series connected) will be the fourfold of a single one.
If you have a flat coil of neglibible thickness with 5 windings, duplicate it with infinitesimal distance between both coils, you also get perfect coupling and thus fourfold inductance of the series circuit. The interesting point is, how fast does the coupling factor decay with windings distance so that the total inductance is somewhere between coupled (fourfold) and uncoupled (doubled) value?
Mathematically, the total inductance of the series circuit is the sum of self and mutual inductance.
Ltot = 2*Lsingle + 2*k*Lsingle, with k varying from 0 to 1.