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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+193)^2 = y^2.
6

%I #21 Jun 13 2015 00:53:43

%S 0,152,203,579,1403,1692,3860,8652,10335,22967,50895,60704,134328,

%T 297104,354275,783387,1732115,2065332,4566380,10095972,12038103,

%U 26615279,58844103,70163672,155125680,342969032,408944315,904139187,1998970475,2383502604,5269709828

%N Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+193)^2 = y^2.

%H Colin Barker, <a href="/A185394/b185394.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

%F G.f.: x^2*(152+51*x+376*x^2-88*x^3-17*x^4-88*x^5)/((1-x)*(1-6*x^3+x^6)). - _Colin Barker_, Aug 04 2012

%t LinearRecurrence[{1,0,6,-6,0,-1,1},{0,152,203,579,1403,1692,3860},70]

%o (PARI) concat(0, Vec(x^2*(88*x^5+17*x^4+88*x^3-376*x^2-51*x-152)/((x-1)*(x^6-6*x^3+1)) + O(x^100))) \\ _Colin Barker_, May 18 2015

%Y Cf. A206426.

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Feb 09 2012