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A144113 Weight array W={w(i,j)} of the natural number array A038722. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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{SUM{w(i,j), i=1,2,...,m, j=1,2,...,n}.

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

A000012, A000027, A144112.

Sequence in context: A085392 A089384 A228812 * A304038 A301983 A165416

Adjacent sequences:  A144110 A144111 A144112 * A144114 A144115 A144116

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 11 2008

STATUS

approved

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Last modified September 21 13:00 EDT 2020. Contains 337272 sequences. (Running on oeis4.)