Option B is correct.
Let m(h) denotes the minimum number of nodes required for height h.
Then the required recursive equation will be :
min nodes in height h = {min nodes in left sub-tree with height h-1} + {(min nodes in left sub-tree with height h-1) – 2} + {root node}
m(h) = {m(h-1)} + {m(h-1) – 2} + {1}.
m(h) = 2 * m(h-1) – 1
Base condition : m(h==1) = 2
m(h) = 2^k * m(h-k) – (2^k -1)
let k = h-1 for base condition.
m(h) = 2^(h-1) +1