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

1,2

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.

Links

Table of n, a(n) for n=1..101.

Formula

row 1: A000027

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

Example

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

Crossrefs

Cf. A000012, A000027, A144112.

Sequence in context: A365138 A228812 A341049 * A370329 A304038 A366113

Adjacent sequences: A144110 A144111 A144112 * A144114 A144115 A144116

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 11 2008

Status

approved