king walk

The Delannoy numbers D(a, b) are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ↑, and ↗). They are given by the recurrence relation D(a, b) = D(a - 1, b) + D(a, b - 1) + D(a - 1, b - 1), with D(0, 0) = 1.

binomial coefficient | Cantor function | Catalan number | integer sequence primes | Motzkin number | Schmidt's problem | Schröder number