The density of ones in Pascalʹs rhombus Original Research Article

Pascalʹs rhombus is a variation of Pascalʹs triangle in which values are computed as the sum of four terms, rather than two. It is shown that the limiting ratio of the number of ones to the number of zeros in Pascalʹs rhombus, taken modulo 2, approaches zero. An asymptotic formula for the number of ones in the rhombus is also shown.