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%I #13 Feb 15 2020 10:52:27
%S 0,44,1121,1317,1541,7644,8780,10080,45621,52241,59817,266960,305544,
%T 349700,1557017,1781901,2039261,9076020,10386740,11886744,52899981,
%U 60539417,69282081,308324744,352850640,403806620,1797049361,2056565301,2353558517,10473972300
%N Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+439)^2 = y^2.
%C Also values x of Pythagorean triples (x, x+439, y).
%C Corresponding values y of solutions (x, y) are in A159890.
%C For the generic case x^2+(x+p)^2 = y^2 with p = m^2-2 a (prime) number > 7 in A028871, see A118337.
%C lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C lim_{n -> infinity} a(n)/a(n-1) = (443+42*sqrt(2))/439 for n mod 3 = {1, 2}.
%C lim_{n -> infinity} a(n)/a(n-1) = (450483+287918*sqrt(2))/439^2 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)+878 for n > 6; a(1)=0, a(2)=44, a(3)=1121, a(4)=1317, a(5)=1541, a(6)=7644.
%F G.f.: x*(44+1077*x+196*x^2-40*x^3-359*x^4-40*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F a(3*k+1) = 439*A001652(k) for k >= 0.
%t LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 44, 1121, 1317, 1541, 7644, 8780}, 50] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2012 *)
%o (PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+878*n+192721), print1(n, ",")))}
%Y Cf. A159890, A028871, A118337, A118675, A118676, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159891 (decimal expansion of (443+42*sqrt(2))/439), A159892 (decimal expansion of (450483+287918*sqrt(2))/439^2).
%K nonn,easy
%O 1,2
%A _Mohamed Bouhamida_, Jun 20 2007
%E Edited and two terms added by _Klaus Brockhaus_, Apr 30 2009
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