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A372667
Norm i^2+j^2+k^2 of (i,j,k) for 0 <= k <= j <= i.
1
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.
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
KEYWORD
nonn,tabf
AUTHOR
A. Timothy Royappa, May 09 2024
EXTENSIONS
More terms from Andrey Zabolotskiy, May 09 2024
STATUS
approved