%I A119869
%S A119869 1,13,19,43,55,79,87,135,141,177,201,225,249,321,321,369,381,429,459,531,
%T A119869 555,603,627,675,683,767,791,887,935,959,959,1055,1061,1157,1205,1253,
               1289,
%U A119869 1409,1433,1481,1505,1553,1601,1721,1745,1865,1865,1961,1985,2093,2123
%N A119869 Sizes of successive clusters in f.c.c. lattice centered at a lattice 
               point.
%D A119869 N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed 
               spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.
%H A119869 N. J. A. Sloane, <a href="b119869.txt">Table of n, a(n) for n = 0..9999</
               a>
%H A119869 Paul Bourke, <a href="http://astronomy.swin.edu.au/~pbourke/geometry/
               waterman/index.html">Waterman Polyhedra.</a>
%H A119869 Paul Bourke, <a href="http://local.wasp.uwa.edu.au/~pbourke/geometry/
               waterman/gen/">On-line generator</a>
%H A119869 Martin Kraus, <a href="http://www.ac-noumea.nc/maths/amc/polyhedr/CCP_.htm">
               Live Graphics3d</a>
%H A119869 Mirek Majewski, <a href="http://www.mupad.com/mathpad/2006/majewski/">
               Dedicated commands in MuPAD</a>
%H A119869 Wouter Meeussen, <a href="http://users.pandora.be/Wouter.Meeussen/ConvexHull3D.m">
               ConvexHull3D package & demo-file.</a>
%H A119869 Mark Newbold, <a href="http://dogfeathers.com/java/ccppoly.html">Waterman 
               Polyhedra.</a> CCPOLY Java Applet.
%H A119869 Steve Waterman, <a href="http://watermanpolyhedron.com/watermanpolyhedra1.html">
               Waterman Polyhedron.</a>
%H A119869 Steve Waterman, <a href="http://watermanpolyhedron.com/MISSING.html">
               Missing numbers formula</a>
%F A119869 Partial sums of A004015, which has an explicit generating function.
%p A119869 maxd:=20001: read format: temp0:=trunc(evalf(sqrt(maxd)))+2: a:=0: for 
               i from -temp0 to temp0 do a:=a+q^( (i+1/2)^2): od: th2:=series(a,
               q,maxd): a:=0: for i from -temp0 to temp0 do a:=a+q^(i^2): od: th3:=series(a,
               q,maxd): th4:=series(subs(q=-q,th3),q,maxd):
%p A119869 t1:=series((th3^3+th4^3)/2,q,maxd): t1:=series(subs(q=sqrt(q),t1),q,floor(maxd/
               2)): t2:=seriestolist(t1): t4:=0; for n from 1 to nops(t2) do t4:=t4+t2[n]; 
               lprint(n-1, t4); od: (N. J. A. Sloane, Aug 09 2006)
%Y A119869 Cf. A004015, A004215, A055039.
%Y A119869 Cf. A055039 [missing polyhedra]. Properties of Waterman polyhedra: A119870 
               [vertices], A119871 [faces], A119872 [edges], A119873 [volume]. Waterman 
               polyhedra with different centers: A119874, A119875, A119876, A119877, 
               A119878.
%Y A119869 Sequence in context: A102907 A096455 A124199 this_sequence A106904 A106903 
               A098413
%Y A119869 Adjacent sequences: A119866 A119867 A119868 this_sequence A119870 A119871 
               A119872
%K A119869 nonn,nice
%O A119869 0,2
%A A119869 Hugo Pfoertner (hugo(AT)pfoertner.org), May 26 2006
%E A119869 Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 09 2006
%E A119869 Additional links from Steve Waterman, Nov 26 2006