Search: id:A005901
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%I A005901 M4834
%S A005901 1,12,42,92,162,252,362,492,642,812,1002,1212,1442,1692,1962,2252,
%T A005901 2562,2892,3242,3612,4002,4412,4842,5292,5762,6252,6762,7292,7842,
%U A005901 8412,9002,9612,10242,10892,11562,12252,12962,13692,14442,15212,16002
%N A005901 Number of points on surface of cuboctahedron (or icosahedron): a(0) = 
               1, for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. 
               or A_3 or D_3 lattice.
%D A005901 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005901 R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series 
               d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 
               325 (Series 1) (1997), 1137-1142.
%D A005901 H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, 
               For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
%D A005901 Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX 
               search code (225) cF4
%D A005901 R. W. Marks and R. B. Fuller, The Dymaxion World of Buckminster Fuller. 
               Anchor, NY, 1973, p. 46.
%D A005901 S. Rosen, Wizard of the Dome: R. Buckminster Fuller; Designer for the 
               Future. Little, Brown, Boston, 1969, p. 109.
%D A005901 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A005901 T. D. Noe, <a href="b005901.txt">Table of n, a(n) for n=0..1000</a>
%H A005901 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 A005901 R. W. Grosse-Kunstleve, <a href="http://cci.lbl.gov/~rwgk/EIS/CS.html">
               Coordination Sequences and Encyclopedia of Integer Sequences</a>
%H A005901 R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, <a href="http:/
               /www.research.att.com/~njas/doc/ac96cs/">Algebraic Description of 
               Coordination Sequences and Exact Topological Densities for Zeolites</
               a>, Acta Cryst., A52 (1996), pp. 879-889.
%H A005901 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 A005901 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 A005901 N. J. A. Sloane, <a href="a000292a.jpg">A portion of the f.c.c. lattice 
               packing.</a>
%H A005901 K. Urner, <a href="http://www.grunch.net/synergetics/virus.html">Microarchitecture 
               of the Virus</a>
%H A005901 <a href="Sindx_Fa.html#fcc">Index entries for sequences related to f.c.c. 
               lattice</a>
%F A005901 G.f. for coordination sequence for A_n lattice is Sum(binomial(n, i)^2*z^i, 
               i=0..n)/(1-z)^n. [Bacher et al.]
%F A005901 a(n+1) = A027599(n+2) + A09277(n+1) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Feb 11 2005
%p A005901 A005901:=-(z+1)*(z**2+8*z+1)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
%o A005901 (PARI) a(n)=if(n<0,0,10*n^2+1+(n>0))
%Y A005901 Cf. A004015.
%Y A005901 Sequence in context: A109275 A085798 A045945 this_sequence A090554 A009948 
               A007586
%Y A005901 Adjacent sequences: A005898 A005899 A005900 this_sequence A005902 A005903 
               A005904
%K A005901 nonn,easy,nice
%O A005901 0,2
%A A005901 N. J. A. Sloane (njas(AT)research.att.com), R. Vaughan

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