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

1,4

Links

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

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.)

Example

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

Mathematica

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

Crossrefs

Cf. A144217.

Sequence in context: A293578 A098489 A128064 * A187881 A344839 A344836

Adjacent sequences: A144214 A144215 A144216 * A144218 A144219 A144220

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 14 2008

Status

approved