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%I #7 Jun 18 2017 02:25:47
%S 0,84,105,309,765,884,2060,4712,5405,12257,27713,31752,71688,161772,
%T 185313,418077,943125,1080332,2436980,5497184,6296885,14204009,
%U 32040185,36701184,82787280,186744132,213910425,482519877,1088424813,1246761572
%N Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+103)^2 = y^2.
%C Corresponding values y of solutions (x, y) are in A157120.
%C lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C lim_{n -> infinity} a(n)/a(n-1) = (11+3*sqrt(2))/(11-3*sqrt(2)) for n mod 3 = {1, 2}.
%C lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*(11-3*sqrt(2))^2/(11+3*sqrt(2))^2 for n mod 3 = 0.
%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 a(n) = 6*a(n-3)-a(n-6)+206 for n > 6; a(1) = 0, a(2) = 84, a(3) = 105, a(4) = 309, a(5) = 765, a(6) = 884.
%F G.f.: x*(84+21*x+204*x^2-48*x^3-7*x^4-48*x^5)/((1-x)*(1-6*x^3+x^6)).
%F a(3*k+1) = 103*A001652(k) for k >= 0.
%o (PARI) {forstep(n=0, 1300000000, [1, 3], if(issquare(2*n^2+206*n+10609), print1(n, ",")))}
%Y Cf. A157120, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A157121 (decimal expansion of 11+3*sqrt(2)), A157122 (decimal expansion of 11-3*sqrt(2)), A157123 (decimal expansion of (11+3*sqrt(2))/(11-3*sqrt(2))).
%K nonn,easy
%O 1,2
%A _Klaus Brockhaus_, Feb 25 2009
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