How to force console to output larger numbers

Question

I am writing a recursive formula and require values when the function has run hundreds of times. At near the 450th - 500th run, the console outputs infinity.

Is it possible to force Java to output a larger value but in scientific notation?

Recursion:

public static void main(String[] args) {
    for (int i = 0; i < 500; i++) {
        System.out.println(Math.pow(3 + 2 * Math.sqrt(2), i)
                + Math.pow(3 - 2 * Math.sqrt(2), i));
    }
}

Output at roughly 450th run:

2.4705373096084562E302
1.4399346668019402E303
8.392554269850795E303
4.891539095230283E304
2.8509979144396616E305
1.661683357711494E306
9.685000354824998E306
5.644831877123849E307
Infinity
Infinity
Infinity
Infinity
Infinity
Infinity
Infinity
Infinity
Infinity

Edit

I have used BigDecimal, as recommended.

    for (int i = 0; i < 500; i++) {
        BigDecimal n = new BigDecimal(Math.pow(3 + 2 * Math.sqrt(2), i)
                + Math.pow(3 - 2 * Math.sqrt(2), i));
        System.out.println(n);
    }

However, now the console spits out :

Exception in thread "main" java.lang.NumberFormatException: Infinite or NaN
at java.math.BigDecimal.<init>(BigDecimal.java:808)
at mathC.Recursion2.main(Recursion2.java:9)

I have read that BigDecimal should be able to store a value that is roughly 8Gb of memory. Since my laptop contains 16Gb of 1600MHz memory, why is this happening? Is this number really 8Gb of memory?

The number before the error is (SO won't let me format this):

56448318771238491045438986070422562722375814412748377586799357549587081845130965398544956161588871436829847442988862310610370686259432485701530038671444090445069088383193741454463060427351807692569019541559990842957532377423388218307948475268885262237809144041880563122951075397138587894276020263963236237312

Answer 1

You could have a look at BigDecimal.

(That doesn't look very recursive, as Fibonacci algorithms go.)