A144113 Weight array W={w(i,j)} of the natural number array A038722.

1, 2, 1, 3, 1, 2, 4, 1, 1, 3, 5, 1, 1, 1, 4, 6, 1, 1, 1, 1, 5, 7, 1, 1, 1, 1, 1, 6, 8, 1, 1, 1, 1, 1, 1, 7, 9, 1, 1, 1, 1, 1, 1, 1, 8, 10, 1, 1, 1, 1, 1, 1, 1, 1, 9, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Clark Kimberling, Sep 11 2008

Keywords

• nonn
• tabl

Comments

In general, let w(i,j) be the weight of the unit square labeled by its northeast vertex (i,j) and for each (m,n), define S(m,n) = Sum_{i=1..m} Sum_{j=1..n} w(i,j).

Then S(m,n) is the weight of the rectangle [0,m]x[0,n]. We call W the weight array of S and we call S the accumulation array of W. For the case at hand, S is the array of natural numbers having the following antidiagonals: (1), then (3,2), then (6,5,4), then (10,9,8,7) and so on.

Examples

			S(2,4)=1+1+2+3+2+1+1+1=14.
		

Crossrefs

Cf. A000012, A000027, A144112.

Formula

row 1: A000027

row n: n-1 followed by A000012, for n>1.