A157927 Joint-rank array of the numbers i^2+j^2, where i>=0, j>=0.

1, 2, 2, 4, 3, 4, 7, 5, 5, 7, 10, 8, 6, 8, 10, 14, 11, 9, 9, 11, 14, 19, 15, 13, 12, 13, 15, 19, 24, 20, 16, 14, 14, 16, 20, 24, 30, 25, 21, 18, 17, 18, 21, 25, 30, 37, 31, 27, 23, 22, 22, 23, 27, 31, 37, 44, 38, 32, 28, 26, 25, 26, 28, 32, 38, 44

Offset: 1

Author

Clark Kimberling, Dec 17 2010

Keywords

• nonn
• tabl

Comments

The definition of joint-rank array given at A182801 is

here extended to arrays R={f(i,j)} for which the numbers

f(i,j) are not necessarily distinct. Specifically, all

duplicates are assigned the same rank when all the numbers

in R are jointly ranked. Let {a(i,j)} denote the

resulting joint-rank array. In case all f(i,j) are

positive integers, a(i,j)=f(i,j)-L(i,j), where L(i,j) is

the number of numbers in R that are <=f(i,j).

(Row 1)=A047808.

Examples

			A corner of the array R={i^2+j^2} is
0....1....4....9...16...
1....2....5...10...17...
4....5....8...13...20...
9...10...13...18...25...
Replace each term of R by its rank:
1....2....4....7...10...
2....3....5....8...11...
4....5....6....9...13...
7....8....9...12...14...
		

Crossrefs

Cf. A182801, A048147.