Search: id:A005899
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%I A005899 M4115
%S A005899 1,6,18,38,66,102,146,198,258,326,402,486,578,678,786,
%T A005899 902,1026,1158,1298,1446,1602,1766,1938,2118,2306,2502,
%U A005899 2706,2918,3138,3366,3602,3846,4098,4358,4626,4902,5186
%N A005899 Number of points on surface of octahedron: a(0) = 1; for n>0, a(n) = 
               4n^2 + 2; coordination sequence for cubic lattice.
%C A005899 Also, the number of regions the plane can be cut into by two overlapping 
               concave (2n)-gons. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), 
               Nov 05 2002
%C A005899 If X is an n-set and Y_i (i=1,2,3) mutually disjoint 2-subsets of X then 
               a(n-5) is equal to the number of 5-subests of X intersecting each 
               Y_i (i=1,2,3). - Milan R. Janjic (agnus(AT)blic.net), Aug 26 2007
%D A005899 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005899 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.
%D A005899 H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, 
               For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
%D A005899 Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX 
               search code (225) cF8
%D A005899 R. W. Marks and R. B. Fuller, The Dymaxion World of Buckminster Fuller. 
               Anchor, NY, 1973, p. 46.
%D A005899 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985),4545-4558.
%H A005899 T. D. Noe, <a href="b005899.txt">Table of n, a(n) for n=0..1000</a>
%H A005899 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A005899 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 A005899 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 A005899 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 A005899 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 A005899 R. W. Grosse-Kunstleve, <a href="http://cci.lbl.gov/~rwgk/EIS/CS.html">
               Coordination Sequences and Encyclopedia of Integer Sequences</a>
%F A005899 G.f.: ((1+x)/(1-x))^3.
%F A005899 Binomial transform of [1, 5, 7, 1, -1, 1, -1, 1,...]. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Nov 02 2007
%p A005899 A005899:=-(z+1)**3/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
%t A005899 s=2;lst={s-1};Do[s+=n+1;AppendTo[lst, s], {n, 3, 6!, 8}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A005899 Partial sums give A001845.
%Y A005899 Sequence in context: A116367 A101853 A132432 this_sequence A129863 A035489 
               A122061
%Y A005899 Adjacent sequences: A005896 A005897 A005898 this_sequence A005900 A005901 
               A005902
%K A005899 nonn,easy,nice
%O A005899 0,2
%A A005899 N. J. A. Sloane (njas(AT)research.att.com).

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