When a problem is being voted on in the Perplexus queue, the journeymen and scholars post comments and vote on the problem. A "thumbs up" (TU) scores +1 point, a "thumbs down" (TD) scores -1, and a comment with no vote scores 0.

Suppose a problem in the queue has A responses and a score of B. Find a formula that gives the number of possible combinations of TU's, TD's and nonvoting comments the problem has received.

Note: For example a problem with 3 responses and a score of +1 has two possibilities: {one TU and two comments} and {two TU's and one TD}