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Search: id:A005902
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| A005902 |
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Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.
(Formerly M4898)
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+0
29
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| 1, 13, 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, 5083, 6525, 8217, 10179, 12431, 14993, 17885, 21127, 24739, 28741, 33153, 37995, 43287, 49049, 55301, 62063, 69355, 77197, 85609, 94611, 104223, 114465, 125357, 136919, 149171
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Called "magic numbers" in some chemical contexts.
Partial sums of A005901(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 30 2003
Equals binomial transform of [1, 12, 30, 20, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 01 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Bjornholm, Clusters..., Contemp. Phys. 31 1990 pp. 309-324.
H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (2).
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
D. R. Herrick, Home Page (displays these numbers as sizes of clusters in chemistry)
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
K. Urner, Cuboctahedral Sphere Packing
Index entries for crystal ball sequences
Index entries for sequences related to f.c.c. lattice
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FORMULA
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(2*n+1)*(5*n^2+5*n+3)/3.
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EXAMPLE
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a(4) = 147 = (1, 3, 3, 1) dot (1, 12, 30, 20) = (1 + 36 + 90 + 20). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 01 2008]
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MAPLE
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A005902 := n -> (2*n+1)*(5*n^2+5*n+3)/3;
A005902:=(z+1)*(z**2+8*z+1)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.
Sequence in context: A027000 A029531 A158485 this_sequence A051798 A061161 A007202
Adjacent sequences: A005899 A005900 A005901 this_sequence A005903 A005904 A005905
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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