Delannoy number
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In mathematics, a Delannoy number describes the number of paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (a, b), using only single steps north, northeast, or east.
For an n × n grid, the first few Delannoy numbers (starting with n=0) are (sequence A001850 in OEIS):
1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, ...
The following figure illustrates the 63 Delannoy paths through a 3 × 3 grid:
The paths that do not rise above the SW–NE diagonal represent the Schröder numbers.
