Java:

public static BigInteger fibonacciModified(int t1, int t2, int n) {
    BigInteger n2 = BigInteger.valueOf(t1), n1 = BigInteger.valueOf(t2), fib = BigInteger.ZERO;
    if (n == 1) {
        return n2;
    }
    if (n == 2) {
        return n1;
    }
    for (int i=3; i <=n; ++i) {
        fib = n2.add(n1.multiply(n1));
        n2 = n1;
        n1 = fib;
    }
    return fib;
}