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Delannoy Number
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Wikipedia
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 :

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.

See also

References

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Last updated on Wednesday February 06, 2008 at 05:17:46 PST (GMT -0800)
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