A short program finds: 3751

If r and s are nonnegative integers that do not exceed N, where N is {0, 1, 2, 3, ... } the sum is the sequence

{1, 12, 91, 600, 3751, 22932, 138811, ... }

which is in Sloane's as  A160869  a(n) = sigma(6^(n-1)).

Although I cannot make the formula given by sigma(6^(n-1)) match the results, which should not be surprising since it is a different formula than the one used in this problem.

-------------------

top = 5

total = 0

for r in range(top):

    for s in range(top):

        total += 2**r*3**s

print(total)

for top in range(1,8):

    total = 0

    for r in range(top):

        for s in range(top):

            total += 2**r*3**s

    print(top-1,total)