(2,1)-Pascal triangle

File:Sister Pascal's Triangle.png

Rows zero to five of (2,1)-Pascal triangle

In mathematics, the (2,1)-Pascal triangle (mirrored Lucas triangle) is a triangular array.

The rows of the (2,1)-Pascal triangle (sequence A029653 in the OEIS) are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows.

The triangle is based on the Pascal's Triangle with the second line being (2,1) and the first cell of each row set to 2.

This construction is related to the binomial coefficients by Pascal's rule, with one of the terms being $2x+y$.

$(2x+y)(x+y{)}^{n-1}$

References

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