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    Delannoy Number

    Alternate name
    Definition

    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.

    Associated person

    Henri Delannoy

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