Search: id:A005918
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%I A005918 M3843
%S A005918 1,5,14,29,50,77,110,149,194,245,302,365,434,509,590,677,770,869,974,1085,
%T A005918 1202,1325,1454,1589,1730,1877,2030,2189,2354,2525,2702,2885,3074,3269,
%U A005918 3470,3677,3890,4109,4334,4565,4802,5045,5294,5549,5810,6077,6350,6629
%N A005918 Number of points on surface of square pyramid: 3*n^2 + 2 (n>0).
%C A005918 Also coordination sequence of the 5-connected net = hexagonal net X integers.
%C A005918 Also (except for initial term) numbers of the form 3n^2+2 that are not 
               squares. See link for proof. - Cino Hilliard (hillcino368(AT)gmail.com), 
               Mar 01 2003
%C A005918 If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) 
               is the number of 4-subsets of X intersecting both Y and Z. - Milan 
               R. Janjic (agnus(AT)blic.net), Sep 08 2007
%D A005918 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005918 H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, 
               For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
%D A005918 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%D A005918 A. F. Wells, Three-Dimensional Nets and Polyhedra, Fig. 15.1 (e).
%H A005918 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A005918 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 A005918 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 A005918 Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/3n2isnotsquare.msnw">
               3n^2+2 not square</a>.
%F A005918 G.f.: (1-x^2)*(1-x^3)/(1-x)^5.
%p A005918 A005918:=-(z+1)*(z**2+z+1)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
%o A005918 (PARI) sq3nsqp2(n) = { for(x=1,n, y = 3*x*x+2; print1(y" ") ) }
%Y A005918 Sequence in context: A005586 A031333 A047801 this_sequence A019262 A076042 
               A049791
%Y A005918 Adjacent sequences: A005915 A005916 A005917 this_sequence A005919 A005920 
               A005921
%K A005918 nonn,easy
%O A005918 0,2
%A A005918 N. J. A. Sloane (njas(AT)research.att.com).
%E A005918 More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003

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