For n hard disks in a strip of width w, the j-th Betti number grows polynomially like n^{2j} when w >= j+2 and exponentially like (q+1)^n n^{qw+2r} when 2 <= w <= j+1.
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Configuration spaces of disks in an infinite strip
For n hard disks in a strip of width w, the j-th Betti number grows polynomially like n^{2j} when w >= j+2 and exponentially like (q+1)^n n^{qw+2r} when 2 <= w <= j+1.