A144217 Weight array of A144216: a rectangular array by antidiagonals.

0, 1, 1, 2, 0, 2, 3, 0, 0, 3, 4, 0, 0, 0, 4, 5, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 7, 8, 0, 0, 0, 0, 0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Clark Kimberling, Sep 14 2008

Keywords

• nonn
• tabl

Examples

			Northwest corner:
0 1 2 3 4 5
1 0 0 0 0 0
2 0 0 0 0 0
3 0 0 0 0 0
4 0 0 0 0 0
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened).

Crossrefs

Cf. A144217.

Programs

Mathematica

Array[Append[PadRight[{#},#,0],#]&,15,0] (* Paolo Xausa, Dec 21 2023 *)

Formula

Start with R(m,n)=(m(m-1)+n(n-1))/2 for m>=1,n>=1. Put R(m,n)=0 if m=0 or n=0. Define w(m,n)=R(m,n)-R(m-1,n-1)-R(m,n-1)-R(m-1,n) for m>=1, n>=1. Then the weight array W={w(m,n)} is A144217. (See A144112.)