Need help on implementation of AI move generation

Hi, I am totally new to Java so please be patient. I am attempting to write a a card-shredding game in java and am currently in the process of writing code for the AI move generation. To generate all combinations of possible moves. I am stuck at this point because I have no idea how to implement it.
The problem is this:
Each card has a suit (Clubs=0, Diamonds=1, Hearts=2, Spades=3)
Each card has a value (Two=2, Three=3...Jack=11, Queen=12...Ace=14)
I need a method in which to generate all possible moves, based on a given vector of cards and an initial card from which to start from. I have written the card and deck classes and most of the game class. Assume you are given a vector of cards each of which have a suit and a value and an initial card to compare from.
E.g.
Initital card = Nine of Diamonds (value=9, suit=1)
Vector of cards= (3 of hearts, 4 of diamonds, 4 of clubs, 6 of diamonds, 8 of diamonds, 9 of spades, 10 of diamonds, 10 of hearts, 10 of clubs, king of diamonds, king of hearts.
Rule1 - From the given initial card, the allowed first card in the combination is any card which meet the following criteria:- (match the suit) or (match the value)
Rule2 - The cards following the second card can match (The same value as the previous card) or (value +1 or -1 of the same suit)
I would be so gratious for any feedback on my problem, I am not asking for code or anything like that, more so an approach. I am unsure of the data structures involved and method to implement this problem. Any advice would be greatly appreciated.

Given your two rules and your example vector there are alot of second cards that can be picked and from that you can use the entire vector for the 3rd card depending on the second.
Ie. there are alot of combinations and I don't want to calculate them all.

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