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A119869
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Sizes of successive clusters in f.c.c. lattice centered at a lattice point.
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8
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1, 13, 19, 43, 55, 79, 87, 135, 141, 177, 201, 225, 249, 321, 321, 369, 381, 429, 459, 531, 555, 603, 627, 675, 683, 767, 791, 887, 935, 959, 959, 1055, 1061, 1157, 1205, 1253, 1289, 1409, 1433, 1481, 1505, 1553, 1601, 1721, 1745, 1865, 1865, 1961, 1985, 2093, 2123
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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.
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..9999
Paul Bourke, Waterman Polyhedra.
Paul Bourke, On-line generator
Martin Kraus, Live Graphics3d
Mirek Majewski, Dedicated commands in MuPAD
Wouter Meeussen, ConvexHull3D package & demo-file.
Mark Newbold, Waterman Polyhedra. CCPOLY Java Applet.
Steve Waterman, Waterman Polyhedron.
Steve Waterman, Missing numbers formula
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FORMULA
| Partial sums of A004015, which has an explicit generating function.
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MAPLE
| 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):
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)
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CROSSREFS
| Cf. A004015, A004215, A055039.
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.
Sequence in context: A029478 A096455 A124199 * A106904 A106903 A098413
Adjacent sequences: A119866 A119867 A119868 * A119870 A119871 A119872
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KEYWORD
| nonn,nice
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), May 26 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 09 2006
Additional links from Steve Waterman, Nov 26 2006
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