%I A088920
%S A088920 2,50,1682,57122,1940450,65918162,2239277042,76069501250,2584123765442,
%T A088920 87784138523762,2982076586042450,101302819786919522,3441313796169221282,
%U A088920 116903366249966604050,3971273138702695316402
%N A088920 Solutions k to the Diophantine equation k = 2n^2 = m^2+1.
%H A088920 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NSWNumber.html">NSW Number</a>
%F A088920 G.f.: (2x^2-20x+2)/[(1-x)(1-34x+x^2)].
%F A088920 a(n) = -(Sinh[(2 n - 1) ArcTanh[Sqrt[2]]])^2 = 1 -(Cosh[(2 n - 1) ArcTanh[Sqrt[2]]])^2 
               [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
%t A088920 Table[Round[N[ -(Sinh[(2 n - 1) ArcTanh[Sqrt[2]]])^2, 100]], {n, 1, 20}] 
               [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
%Y A088920 Corresponding solutions of n are A001653 and m are A002315.
%Y A088920 A008843(n-1) + 1.
%Y A088920 Sequence in context: A083939 A083941 A080263 this_sequence A079198 A080293 
               A084107
%Y A088920 Adjacent sequences: A088917 A088918 A088919 this_sequence A088921 A088922 
               A088923
%K A088920 nonn
%O A088920 1,1
%A A088920 Eric Weisstein (eric(AT)weisstein.com), Oct 23, 2003