This shows how to do the iteration using indexing and a loop instead of typing out each iteration manually:
I'm not sure that this gives the right answer as the volume calculation
based on your original
doesn't seem to include the 'volume of air in the tyre' which I called V0.
After the first iteration, the pressure volume relationship seems reasonable, though (see plot below).
You should be able to adapt this to make necessary corrections.
V0 = 0.03;
T = 300;
P0 = 100000;
S = 0.02;
B = 0.018;
Vc = pi/4 * B^2 * S;
P(1) = P0;
P(2) = P0 * ((V0 + Vc) / V0)^1.35;
V(1) = V0;
idx = 2;
while P(end) < 400000
V(idx) = P0*Vc / P(idx);
P(idx+1) = P(idx) * ((V(idx) + V0) / V0)^1.35;
idx = idx + 1;
V(end+1) = P0*Vc / P(end);