Search: id:A119874
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%I A119874
%S A119874 6,14,38,38,68,92,116,116,164,188,236,236,266,298,370,370,418,466,490,
%T A119874 490,586,610,682,682,736,784,856,856,904,976,1048,1048,1144,1168,1264,
%U A119874 1264,1312,1368,1464,1464,1566,1638,1686,1686,1830,1878,1926,1926,1974
%N A119874 Sizes of successive clusters in f.c.c. lattice centered at an octahedral 
               hole.
%D A119874 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 A119874 N. J. A. Sloane, <a href="b119874.txt">Table of n, a(n) for n = 0..9999</
               a>
%H A119874 Wouter Meeussen, <a href="http://users.pandora.be/Wouter.Meeussen/ConvexHull3D.m">
               ConvexHull3D package & demo-file.</a>
%F A119874 Partial sums of A005887, which has an explicit generating function.
%p A119874 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 A119874 t1:=series((th3^3-th4^3)/(2*q),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 A119874 Cf. A005887.
%Y A119874 Cf. A119869, Properties of Waterman polyhedra of void center type: A119875 
               [vertices], A119876 [faces], A119877 [edges], A119878 [volume].
%Y A119874 Sequence in context: A066510 A036387 A053560 this_sequence A134259 A069166 
               A015892
%Y A119874 Adjacent sequences: A119871 A119872 A119873 this_sequence A119875 A119876 
               A119877
%K A119874 nonn
%O A119874 0,1
%A A119874 Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 05 2006
%E A119874 Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 09 2006

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