%I A051047
%S A051047 1,3,8,120,1680,23408,326040,4541160,63250208,880961760,12270214440,
%T A051047 170902040408,2380358351280,33154114877520,461777249934008,
%U A051047 6431727384198600,89582406128846400,1247721958419651008
%N A051047 For definition see Mathematica code.
%C A051047 The recurrence gives an infinite sequence of polynomials S={x,x+2,c_1(x),
               c_2(x),...} such that the product of any two consecutive polynomials, 
               increased by 1, is the square of a polynomial - see the Jones reference.
%D A051047 Jones, B. W. "A Variation of a Problem of Davenport and Diophantus." 
               Quart. J. Math. (Oxford) Ser. (2) 27, 349-353, 1976.
%H A051047 Andrej Dujella and Attila Petho, <a href="http://citeseerx.ist.psu.edu/
               viewdoc/download?doi=10.1.1.59.3785&rep=rep1&type=pdf">Generalization 
               of a theorem of Baker and Davenport</a> [From William Stein, Oct 
               24 2009]
%t A051047 With[{x = 1},
%t A051047 Join[{x, x + 2},
%t A051047 RecurrenceTable[{c[-1] == c[0] == 0,
%t A051047 c[k] == (4 x^2 + 8 x + 2) c[k - 1] - c[k - 2] + 4 (x + 1)}, c, {k, 1, 
               12}]]]
%Y A051047 Cf. A051048. Essentially the same as A045899.
%Y A051047 Sequence in context: A123279 A134803 A030063 this_sequence A036504 A132491 
               A083112
%Y A051047 Adjacent sequences: A051044 A051045 A051046 this_sequence A051048 A051049 
               A051050
%K A051047 nonn
%O A051047 1,2
%A A051047 Eric Weisstein (eric(AT)weisstein.com)
%E A051047 Entry revised by N. J. A. Sloane, Oct 25 2009, following correspondence 
               with Eric Weisstein