%I A129625
%S A129625 0,75,432,699,1092,3115,4660,6943,18724,27727,41032,109695,162168,
%T A129625 239715,639912,945747,1397724,3730243,5512780,8147095,21742012,32131399,
%U A129625 47485312,126722295,187276080,276765243,738592224,1091525547,1613106612
%N A129625 Nonnegative values x of solutions (x, y) to the Diophantine equation 
               x^2+(x+233)^2 = y^2.
%C A129625 Also values x of Pythagorean triples (x, x+233, y).
%C A129625 Corresponding values y of solutions (x, y) are in A157297.
%C A129625 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A129625 lim_{n -> infinity} a(n)/a(n-1) = (251+66*sqrt(2))/233 for n mod 3 = 
               {1, 2}.
%C A129625 lim_{n -> infinity} a(n)/a(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 
               3 = 0.
%F A129625 a(n) = 6*a(n-3)-a(n-6)+466 for n > 6; a(1)=0, a(2)=75, a(3)=432, a(4)=699, 
               a(5)=1092, a(6)=3115.
%F A129625 G.f.: x*(75+357*x+267*x^2-57*x^3-119*x^4-57*x^5)/((1-x)*(1-6*x^3+x^6)).
%F A129625 a(3*k+1) = 233*A001652(k) for k >= 0.
%o A129625 (PARI) {forstep(n=0, 1700000000, [3, 1], if(issquare(2*n^2+466*n+54289), 
               print1(n, ",")))}
%Y A129625 Cf. A157297, A001652, A129288, A129289, A129298, A156035 (decimal expansion 
               of 3+2*sqrt(2)), A157298 (decimal expansion of (251+66*sqrt(2))/233), 
               A157299 (decimal expansion of (82611+44030*sqrt(2))/233^2).
%Y A129625 Sequence in context: A158765 A055561 A015223 this_sequence A133382 A017791 
               A017738
%Y A129625 Adjacent sequences: A129622 A129623 A129624 this_sequence A129626 A129627 
               A129628
%K A129625 nonn
%O A129625 1,2
%A A129625 Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 30 2007
%E A129625 Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Apr 11 2009