I have the following recursion equation
$T(1,n) = 1, (n > 0)$
$T(a,1) = \infty, (a > 1)$
$T(a,n) = \min[ T(b,n) + T(b,n-1) + T(a-b,n-1)], 1 \leq b < a$
How can the closed form be derived for the equation? Or alternatively is there any material out there regarding recursion equations with min in them?