Consider all "integer" points in the 1st Quadrant, i.e. North-East part of the coordinates system.

How many lattice paths from (0,0) to (b,a) exist if only east (1,0), north (0,1), and northeast (1,1) steps are allowed?

Provide a general recurrence formula, supported by few samples, say all (a,b) points between (0,0) and (6,6).

What can be said about the numbers thus obtained?

Try to formulate a direct formula for the integer points on the y=x line, i.e. D(m,m)=...