login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144112 Weight array W={w(i,j)} of the natural number array A000027. 63
1, 1, 2, 2, 1, 3, 3, 1, 1, 4, 4, 1, 1, 1, 5, 5, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The lattice lines in the first quadrant (including the x and y axes) cut the plane into unit squares.  Suppose a weight w(i,j) is assigned to the square that has as upper right corner the point (i,j).  Let s(m,n) be the sum of the weights w(i,j) for 1<=i<=m, 1<=j<=n.  We call the array W={w(i,j)} the weight array of the array S={s(m,n)} and S the accumulation array of W.  For the case at hand, S is the array of natural numbers having the following antidiagonals: (1), then (2,3), then (4,5,6), then (7,8,9,10) and so on.

Contribution from Clark Kimberling, Sep 14 2008: (Start)

In general, the weight array W of an arbitrary rectangular array S={s(i,j): i>=1, j>=1} is defined in two steps:

(1) extend s by defining s(i,j)=0 if i=0 or j=0;

(2) then w(m,n)=s(m,n)+s(m-1,n-1)-s(m,n-1)-s(m-1,n) for m>=1, n>=1. (End)

LINKS

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

FORMULA

row 1: 1 followed by A000027

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

EXAMPLE

Northwest corner:

1 1 2 3 4 5

2 1 1 1 1 1

3 1 1 1 1 1

4 1 1 1 1 1

5 1 1 1 1 1.

so that the accumulation array has corner

1...2...4...7...11...16

3...5...8...12..17...23

6...9...13..18..24...31

10..14..19..25..32...40

15..20..26..33..41...50.

s(2,4)=1+1+2+3+2+1+1+1=12.

CROSSREFS

Cf. A000012, A000027.

Sequence in context: A103360 A267409 A104469 * A178568 A104660 A212125

Adjacent sequences:  A144109 A144110 A144111 * A144113 A144114 A144115

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 11 2008

EXTENSIONS

Example by Clark Kimberling, Jan 31 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 16:53 EDT 2018. Contains 316529 sequences. (Running on oeis4.)