Search: id:A005902
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%I A005902 M4898
%S A005902 1,13,55,147,309,561,923,1415,2057,2869,3871,5083,6525,8217,10179,
%T A005902 12431,14993,17885,21127,24739,28741,33153,37995,43287,49049,55301,
%U A005902 62063,69355,77197,85609,94611,104223,114465,125357,136919,149171
%N A005902 Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence 
               for f.c.c. lattice.
%C A005902 Called "magic numbers" in some chemical contexts.
%C A005902 Partial sums of A005901(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Oct 30 2003
%C A005902 Equals binomial transform of [1, 12, 30, 20, 0, 0, 0,...] [From Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Aug 01 2008]
%D A005902 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005902 S. Bjornholm, Clusters..., Contemp. Phys. 31 1990 pp. 309-324.
%D A005902 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.
%D A005902 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (2).
%D A005902 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A005902 T. D. Noe, <a href="b005902.txt">Table of n, a(n) for n=0..1000</a>
%H A005902 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination 
               Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http:/
               /www.research.att.com/~njas/doc/ldl7.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.ps">ps</a>).
%H A005902 D. R. Herrick, <a href="http://www.uoregon.edu/~chem/herrick.html">Home 
               Page</a> (displays these numbers as sizes of clusters in chemistry)
%H A005902 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005902 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005902 K. Urner, <a href="http://www.4dsolutions.net/ocn/sphpack2.html">Cuboctahedral 
               Sphere Packing</a>
%H A005902 <a href="Sindx_Cor.html#crystal_ball">Index entries for crystal ball 
               sequences</a>
%H A005902 <a href="Sindx_Fa.html#fcc">Index entries for sequences related to f.c.c. 
               lattice</a>
%F A005902 (2*n+1)*(5*n^2+5*n+3)/3.
%e A005902 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]
%p A005902 A005902 := n -> (2*n+1)*(5*n^2+5*n+3)/3;
%p A005902 A005902:=(z+1)*(z**2+8*z+1)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]
%Y A005902 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.
%Y A005902 Sequence in context: A027000 A029531 A158485 this_sequence A051798 A061161 
               A007202
%Y A005902 Adjacent sequences: A005899 A005900 A005901 this_sequence A005903 A005904 
               A005905
%K A005902 nonn,easy,nice
%O A005902 0,2
%A A005902 N. J. A. Sloane (njas(AT)research.att.com).

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