Delannoy Number Carpet

size

64

mod

3

hue
mesh

The Delannoy number

(x,y)

gives the number of ways to reach point

{x,y}

(with non-negative integer coordinates) from the origin using only certain moves. They may be either up

{0,1}

, to the right

{1,0}

or one step along the diagonal

{1,1}

. Plots of

(x,y)modn

show nested fractal patterns.