Question

Block Walking and Counting Subsets A Delannoy path in the first quadrant is a walk that uses any of 3 kinds of steps: Up (0,1), Right (1,0), and Diagonal (1, 1). Let D(x, y) be the number of Delannoy paths from (0,0) to (x, y). (a). Find a recurrence relation that gives D(x, y) in terms of smaller values. (b). Find the number of Delannoy paths from (0, 0) to (7,3) c). Find a formula for D(n,1), where n is any whole number. (d*). (for fun!) Find a recurrence and conjecture a formula for D(n, 2), where n is any whole number. Note: you do not need to hand this part in.

Answer 1

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Adding aul the above equations D (n,2), フ