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Search: id:A119874
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| A119874 |
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Sizes of successive clusters in f.c.c. lattice centered at an octahedral hole. |
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+0
7
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| 6, 14, 38, 38, 68, 92, 116, 116, 164, 188, 236, 236, 266, 298, 370, 370, 418, 466, 490, 490, 586, 610, 682, 682, 736, 784, 856, 856, 904, 976, 1048, 1048, 1144, 1168, 1264, 1264, 1312, 1368, 1464, 1464, 1566, 1638, 1686, 1686, 1830, 1878, 1926, 1926, 1974
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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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
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N. J. A. Sloane, Table of n, a(n) for n = 0..9999
Wouter Meeussen, ConvexHull3D package & demo-file.
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FORMULA
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Partial sums of A005887, which has an explicit generating function.
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MAPLE
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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), 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
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Cf. A005887.
Cf. A119869, Properties of Waterman polyhedra of void center type: A119875 [vertices], A119876 [faces], A119877 [edges], A119878 [volume].
Sequence in context: A066510 A036387 A053560 this_sequence A134259 A069166 A015892
Adjacent sequences: A119871 A119872 A119873 this_sequence A119875 A119876 A119877
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 05 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 09 2006
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