%I A045899
%S A045899 0,8,120,1680,23408,326040,4541160,63250208,880961760,12270214440,
%T A045899 170902040408,2380358351280,33154114877520,461777249934008,
%U A045899 6431727384198600
%N A045899 Numbers n such that n+1 and 3*n+1 are perfect squares.
%D A045899 A. Baker and H. Davenport, The equations 3x^2-2=y^2 and 8x^2-7=z^2, Quart. 
               J. Math. Oxford Ser. (2) 20 (1969), 129-137.
%D A045899 A. Dujella and A. Pethoe, A generalization of a theorem of Baker and 
               Davenport, Quart. J. Math. Oxford Ser. (2) 49 (1998), 291-306.
%H A045899 A. Dujella, <a href="http://www.math.hr/~duje/ddbib.html">The Problem 
               of Diophantus and Davenport, References</a>
%H A045899 A. Dujella, <a href="http://www.math.hr/~duje/papers.html">Publications 
               of Andrej Dujella</a>
%H A045899 P. Gibbs, <a href="http://www.weburbia.demon.co.uk/pg/diophant.htm">1,
               3,8,120 ... A Diophantine Problem</a>
%H A045899 P. Gibbs, <a href="http://arXiv.org/abs/math.NT/0107203">Diophantine 
               quadruples and Cayley's hyperdeterminant</a>.
%F A045899 a(k)=14*a(k-1)-a(k-2)+8
%F A045899 a[k] = ((Sqrt[3]+2)*(7+4*Sqrt[3])^k - (Sqrt[3]-2)(7-4*Sqrt[3])^k - 4)/
               6 - Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 23 2006
%t A045899 FullSimplify[Table[((Sqrt[3]+2)*(7+4*Sqrt[3])^k - (Sqrt[3]-2)(7-4*Sqrt[3])^k 
               - 4)/6, {k, 0, 40}]] - Joseph Biberstine (jrbibers(AT)indiana.edu), 
               Apr 23 2006
%Y A045899 Equals A046184(n+1) - 1.
%Y A045899 Essentially the same as A051047. Cf. A067900.
%Y A045899 Sequence in context: A116008 A086302 A053129 this_sequence A165231 A004381 
               A166179
%Y A045899 Adjacent sequences: A045896 A045897 A045898 this_sequence A045900 A045901 
               A045902
%K A045899 nonn
%O A045899 1,2
%A A045899 Andrej Dujella (duje(AT)math.hr)