A047808 -id:A047808 - cp's OEIS frontend

A047809 a(n) counts different values of i^2+j^2+k^2 <= n^2 or number of distances from the origin to all integer points inside a sphere of radius n.

1, 2, 5, 9, 15, 23, 32, 43, 55, 70, 86, 103, 122, 143, 166, 190, 215, 243, 273, 304, 336, 371, 406, 443, 482, 523, 566, 611, 656, 704, 753, 803, 855, 910, 966, 1024, 1083, 1145, 1207, 1270, 1336, 1404, 1474, 1544, 1616, 1690, 1766, 1843, 1922, 2004

Offset: 0

Wouter Meeussen,_David W. Wilson_

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A047808, A000378.

Table[ Length@Union@Flatten@Table[ i^2+j^2+k^2, {i, 0, n}, {j, 0, Min[ i, Floor[ Sqrt[ n^2-i^2 ] ] ]}, {k, 0, Min[ j, Floor[ Sqrt[ n^2-i^2-j^2 ] ] ]} ], {n, 0, 64} ]

a(n) = number of b(i) <= n^2, b() = A000378.

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

Original entry on oeis.org

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

Clark Kimberling, Dec 17 2010

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.

			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...

Cf. A182801, A048147.

cp's OEIS Frontend

A047809 a(n) counts different values of i^2+j^2+k^2 <= n^2 or number of distances from the origin to all integer points inside a sphere of radius n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Crossrefs