LeafCount[f[k]] for particular small integers k returns the number 2^(k+1)-1. e.g. for k=3, it returns 15.
But it returns the same answer for k=30, 31, .... It returns 2147483647, which, probably not coincidentally, is 2^31-1.
ByteCount has a similar problem in running out of bits in its counter.
Anyway, ByteCount also lies in a different way... because it doesn't take into account the sharing that (say) f has. Without the sharing implicit in the formula above, I could not compute that -- it has 2.36 X 10^21 leaves. They are just not different leaves.
I would expect that a 64-bit system might work for k=31, but would conk out somewhere else.