assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?
explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 × 1 × 1 – 1 ) = 0 + 0 + 4 × 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 × 2 × 2 – 1 ) = 32 + 32 + 4 × 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 × 4 × 4 – 1 ) = 204 + 204 + 4 × 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 × 8 × 8 – 1 ) = 980 + 980 + 4 × 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 × 16 × 1 – 1 ) = 4260 + 0 + 4 × 143 = 4832 answer : a
add(add(add(add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4)), add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))), multiply(add(multiply(add(const_4, const_1), const_100), subtract(add(multiply(17, const_4), 9), const_2)), const_4)), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))