Invitation to the party

//used this program solving http://puzzling.stackexchange.com/questions/22353/invitation-to-the-party

import java.math.BigInteger;
import java.util.HashMap;

public class Main {
    static HashMap<Integer,BigInteger> cache = new HashMap<Integer, BigInteger>();

    public static void main(String[] args) {
        cache.put(1, BigInteger.ONE);
        cache.put(2, BigInteger.ONE);
        cache.put(3, BigInteger.valueOf(2l));
        cache.put(4, BigInteger.valueOf(3l));
        cache.put(5, BigInteger.valueOf(3l));
        cache.put(6, BigInteger.valueOf(5l));

        System.out.println(totalInvites(24));
        System.out.println(totalInvites(25));
        System.out.println(totalInvites(180));
    }

    public static BigInteger invites(int minutes) {
        if (!cache.containsKey(minutes)) {
            cache.put(minutes, invites(minutes - 1).add(invites(minutes - 3)).add(invites(minutes - 6)));
        }
        return cache.get(minutes);
    }

    public static BigInteger totalInvites(int minutes) {
        BigInteger result = BigInteger.ZERO;
        for (int i=1; i<=minutes;i++) {
            result = result.add(invites(i));
        }
        return result;
    }
}