Search: id:A005897
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%I A005897 M4497
%S A005897 1,8,26,56,98,152,218,296,386,488,602,728,866,1016,1178,1352,1538,
%T A005897 1736,1946,2168,2402,2648,2906,3176,3458,3752,4058,4376,4706,5048,
%U A005897 5402,5768,6146,6536,6938,7352,7778,8216,8666,9128,9602,10088,10586
%N A005897 a(0) = 1, a(n) = 6n^2 + 2 for n > 0.
%C A005897 Number of points on surface of 3-dimensional cube in which each face 
               has a square grid of dots drawn on it (with n+1 points along each 
               edge, including the corners).
%C A005897 Coordination sequence for b.c.c. lattice.
%D A005897 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005897 H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, 
               For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
%D A005897 Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX 
               search code (194) hP4
%D A005897 R. W. Marks and R. B. Fuller, The Dymaxion World of Buckminster Fuller. 
               Anchor, NY, 1973, p. 46.
%D A005897 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A005897 R. W. Grosse-Kunstleve, <a href="http://cci.lbl.gov/~rwgk/EIS/CS.html">
               Coordination Sequences and Encyclopedia of Integer Sequences</a>
%H A005897 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 A005897 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 A005897 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 A005897 <a href="Sindx_Ba.html#bcc">Index entries for sequences related to b.c.c. 
               lattice</a>
%F A005897 Binomial transform of [1, 7, 11, 1, -1, 1, -1, 1,...]. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Oct 22 2007
%F A005897 a(0) = 1, a(n) = (n+1)^3 - (n-1)^3. - Ilya Nikulshin (ilyanik(AT)gmail.com), 
               Aug 11 2009
%e A005897 For n = 1 we get the 8 corners of the cube; for n = 2 each face has 9 
               points, for a total of 8 + 12 + 6 = 26.
%p A005897 A005897:=-(z+1)*(z**2+4*z+1)/(z-1)**3; [Conjectured (correctly) by S. 
               Plouffe in his 1992 dissertation.]
%Y A005897 Sequence in context: A074238 A126264 A085690 this_sequence A111694 A129111 
               A002413
%Y A005897 Adjacent sequences: A005894 A005895 A005896 this_sequence A005898 A005899 
               A005900
%K A005897 nonn,easy,nice
%O A005897 0,2
%A A005897 N. J. A. Sloane (njas(AT)research.att.com), rwgk(AT)cci.lbl.gov (R.W. 
               Grosse-Kunstleve)

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