A372667 Norm i^2+j^2+k^2 of (i,j,k) for 0 <= k <= j <= i.

0, 1, 2, 3, 4, 5, 6, 8, 9, 12, 9, 10, 11, 13, 14, 17, 18, 19, 22, 27, 16, 17, 18, 20, 21, 24, 25, 26, 29, 34, 32, 33, 36, 41, 48, 25, 26, 27, 29, 30, 33, 34, 35, 38, 43, 41, 42, 45, 50, 57, 50, 51, 54, 59, 66, 75, 36, 37, 38, 40, 41, 44, 45, 46, 49, 54, 52, 53

Offset

0,3

Comments

In crystallography, these triples (i,j,k) can be interpreted as Miller indices, which can be sorted into a list: (0 0 0), (1 0 0), (1 1 0), (1 1 1), (2 0 0), (2 1 0), (2 1 1), (2 2 0), (2 2 1), (2 2 2), (3 0 0), (3 1 0), (3 1 1), (3 2 0), etc.

References

C. Suryanarayana and M. Grant Norton, X-Ray Diffraction - A Practical Approach, Springer Science + Business Media, 1998, p. 83.

Links

Table of n, a(n) for n=0..67.

S. Phil Ahrenkiel, List of the first few Miller indices, in order, excluding (0 0 0)

Example

The first few triples are:
   0, 0, 0
   1, 0, 0
   1, 1, 0
   1, 1, 1
   2, 0, 0
   2, 1, 0
   2, 1, 1
   2, 2, 0
   2, 2, 1
   2, 2, 2
   3, 0, 0
   ...

Maple

a:=[];
for i from 0 to 10 do for j from 0 to i do for k from 0 to j do
a:=[op(a), i^2+j^2+k^2]; od: od: od: a; # N. J. A. Sloane, Jun 03 2024

Prog

(Python)
print([i**2 + j**2 + k**2 for i in range(7) for j in range(i+1) for k in range(j+1)]) # Andrey Zabolotskiy, May 09 2024

Crossrefs

The table of triples forms A331195.

Cf. A070770, A069011 (2-dimensional analog), A004215 (complement to this sequence)

Sequence in context: A235592 A100054 A330193 * A101271 A093110 A165707

Adjacent sequences: A372664 A372665 A372666 * A372668 A372669 A372670

Keyword

nonn,tabf

Author

A. Timothy Royappa, May 09 2024

Extensions

More terms from Andrey Zabolotskiy, May 09 2024

Status

approved