%I A051890
%S A051890 2,2,6,14,26,42,62,86,114,146,182,222,266,314,366,422,482,546,614,
%T A051890 686,762,842,926,1014,1106,1202,1302,1406,1514,1626,1742,1862,1986,
%U A051890 2114,2246,2382,2522,2666,2814,2966,3122,3282,3446,3614,3786,3962
%N A051890 2*(n^2-n+1).
%C A051890 Draw n ellipses in the plane (n>0), any 2 meeting in 4 points; sequence 
               gives number of regions into which the plane is divided.
%C A051890 Least k such that Z(k,2) <= Z(n,3) where Z(m,s) = sum(i>=m, 1/i^s) = 
               zeta(s)-sum(i=1,m-1,1/i^s). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 29 2002
%C A051890 For n>2, third diagonal of [A154685] [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Jan 25 2009]
%D A051890 Parabola, vol. 20, no. 2, 1984, p. 27, Problem #Q607.
%D A051890 J. V. Post, "When Centered Polygonal Numbers are Perfect Squares" preprint.
%H A051890 Parabola, <a href="http://www.maths.unsw.edu.au/Parabola/">Web site</
               a>
%H A051890 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PlaneDivisionbyEllipses.html">Plane Division by Ellipses</a>
%F A051890 a(n)=4*binomial(n, 2)+2. - Francois Jooste (phukraut(AT)hotmail.com), 
               Mar 05 2003
%F A051890 For n>2 nearest integer to sum(k>=n, 1/k^3)/sum(k>=n, 1/k^5) - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Jun 12 2003
%F A051890 a(n) = 2*A002061(n). - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 
               19 2005
%F A051890 a(n)=4*n+a(n-1)-8 (with a(1)=2) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 11 2009]
%e A051890 For n=2, a(2)=4*2+2-8=2; n=3, a(3)=4*3+2-8=6; n=4, a(4)=4*4+6-8=14 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 11 2009]
%p A051890 A051890 := n->2*(n^2-n+1);
%t A051890 a=2;lst={};Do[a+=n;AppendTo[lst,a],{n,0,6!,4}];lst...and/or... lst={};
               Do[AppendTo[lst,2*(n^2-n+1)],{n,5!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Mar 01 2009]
%Y A051890 Cf. A001844, A002061, A014206, A002061.
%Y A051890 Cf. A154685 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 
               25 2009]
%Y A051890 Sequence in context: A049952 A019100 A019101 this_sequence A071109 A005310 
               A002203
%Y A051890 Adjacent sequences: A051887 A051888 A051889 this_sequence A051891 A051892 
               A051893
%K A051890 nonn,new
%O A051890 0,1
%A A051890 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 30 2000