distances in cubic latt{i,u}ce

[Wouter Meeussen]

for what it's worth,

the expression r^2  =  i^2+j^2+k^2 for i,j,k in [0,n] can produce
a limited set of different results : different 'coordination spheres'
around the origin. Their number as a function of n is :
 
In[]:=Table[Length at Union[Flatten[ Table[i^2+j^2+k^2,{i,0,n},{j,0,n},{k,0,n}]
]],
             {n,0,18}]
Out[ ]= {1,4,10,19,32,45,67,88,116,145,179,212,260,300,347,402,464,517,592}

checking EIS tells us it is indeed sandwiched between "coordination
sequences" of real world latt{i,u}ces, but my "dumb" one seems to be missing.

grin,grin,


wouter.



----------------------
%I A027371
%S A027371 1,4,10,19,31,50,82,107,132,168,209,262,319,352,406,481,552,622,680,
%T A027371 766,847,950,1045,1110,1217,1339,1452,1568,1656,1769,1924,2062,2208,
%U A027371 2307,2437,2606,2789,2942,3056,3231,3403,3598,3800,3921,4087,4342,4535
%N A027371 Coordination sequence T3 for Zeolite Code ITE.
%O A027371 0,2
%K A027371 nonn
%A A027371 rwgk at laplace.csb.yale.edu (R.W. Grosse-Kunstleve)
%H A027371 Intl. Zeolite Assn. (Structure Commission)
%H A027371 Coordination Sequences & Encyclopedia of Integer Sequences

----------------------
%I A009868
%S A009868 1,4,10,19,32,50,73,101,132,164,199,240,293,350,394,443,510,587,666,
%T A009868 730,791,879,984,1074,1154,1250,1357,1470,1589,1697,1801,1922,2061,
%U A009868 2196,2326,2464,2600,2754,2914,3058,3215,3376,3550,3727,3886,4071,4252
%N A009868 Coordination sequence T1 for Zeolite Code CON.
%O A009868 0,2
%K A009868 nonn
%A A009868 rwgk at laplace.csb.yale.edu (R.W. Grosse-Kunstleve)
%D A009868 W.M. Meier, D.H. Olson & Ch. Baerlocher, Atlas of Zeolite
Structure Types, 4th Ed., Elsevier, 1996
%D A009868 R.W. Grosse-Kunstleve et al., Algebraic Description of
Coordination Sequences and Exact Topological Densities for Zeolites, Acta
Cryst. submitted.
%H A009868 Coordination Sequences & Encyclopedia of Integer Sequences
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be