Function Repository Resource:

# DelannoyD

Evaluate the Delannoy number

Contributed by: Jan Mangaldan
 ResourceFunction["DelannoyD"][n,m] gives the Delannoy number D(n,m).

## Details

Integer mathematical function, suitable for both symbolic and numerical manipulation.
D(n,m) counts the number of lattice paths from {0,0} to {m,n} in which only east, north and northeast steps are allowed.
ResourceFunction["DelannoyD"] automatically threads over lists.

## Examples

### Basic Examples (1)

Evaluate a Delannoy number:

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### Scope (1)

DelannoyD threads elementwise over lists:

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### Applications (2)

Plot Delannoy numbers on a logarithmic scale:

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Find a formula for the central Delannoy numbers:

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### Properties and Relations (2)

Generate values from the generating function:

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Express the Delannoy number as a finite sum:

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### Neat Examples (1)

Fractal-like pattern generated by a Delannoy number mod 7:

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## Version History

• 1.0.0 – 17 May 2021