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

%I A372667 #29 Apr 09 2025 20:23:52
%S A372667 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,
%T A372667 25,26,29,34,32,33,36,41,48,25,26,27,29,30,33,34,35,38,43,41,42,45,50,
%U A372667 57,50,51,54,59,66,75,36,37,38,40,41,44,45,46,49,54,52,53
%N A372667 Norm i^2+j^2+k^2 of (i,j,k) for 0 <= k <= j <= i.
%C A372667 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.
%D A372667 C. Suryanarayana and M. Grant Norton, X-Ray Diffraction - A Practical Approach, Springer Science + Business Media, 1998, p. 83.
%H A372667 Robert Israel, <a href="/A372667/b372667.txt">Table of n, a(n) for n = 0..10000</a>
%H A372667 S. Phil Ahrenkiel, <a href="http://ahrenkiel.sdsmt.edu/courses/Fall2016/NANO703/lectures/Ch18/TEM_Ch18_91.pdf">List of the first few Miller indices, in order, excluding (0 0 0)</a>
%e A372667 The first few triples are:
%e A372667    0, 0, 0
%e A372667    1, 0, 0
%e A372667    1, 1, 0
%e A372667    1, 1, 1
%e A372667    2, 0, 0
%e A372667    2, 1, 0
%e A372667    2, 1, 1
%e A372667    2, 2, 0
%e A372667    2, 2, 1
%e A372667    2, 2, 2
%e A372667    3, 0, 0
%e A372667    ...
%p A372667 a:=[];
%p A372667 for i from 0 to 10 do for j from 0 to i do for k from 0 to j do
%p A372667 a:=[op(a),i^2+j^2+k^2]; od: od: od: a; # _N. J. A. Sloane_, Jun 03 2024
%o A372667 (Python)
%o A372667 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
%Y A372667 The table of triples forms A331195.
%Y A372667 Cf. A070770, A069011 (2-dimensional analog), A004215 (complement to this sequence)
%K A372667 nonn,tabf
%O A372667 0,3
%A A372667 _A. Timothy Royappa_, May 09 2024
%E A372667 More terms from _Andrey Zabolotskiy_, May 09 2024