cp's OEIS Frontend

A129974 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+937)^2 = y^2.

%I A129974 #9 Feb 15 2020 10:52:27
%S A129974 0,627,1128,2811,6188,9027,18740,38375,54908,111503,225936,322295,
%T A129974 652152,1319115,1880736,3803283,7690628,10963995,22169420,44826527,
%U A129974 63905108,129215111,261270408,372468527,753123120,1522797795,2170907928
%N A129974 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+937)^2 = y^2.
%C A129974 Also values x of Pythagorean triples (x, x+937, y).
%C A129974 Corresponding values y of solutions (x, y) are in A160209.
%C A129974 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A129974 lim_{n -> infinity} a(n)/a(n-1) = (1179+506*sqrt(2))/937 for n mod 3 = {1, 2}.
%C A129974 lim_{n -> infinity} a(n)/a(n-1) = (933747+224782*sqrt(2))/937^2 for n mod 3 = 0.
%H A129974 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
%F A129974 a(n) = 6*a(n-3)-a(n-6)+1874 for n > 6; a(1)=0, a(2)=627, a(3)=1128, a(4)=2811, a(5)=6188, a(6)=9027.
%F A129974 G.f.: x*(627+501*x+1683*x^2-385*x^3-167*x^4-385*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F A129974 a(3*k+1) = 937*A001652(k) for k >= 0.
%o A129974 (PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1874*n+877969), print1(n, ",")))}
%Y A129974 Cf. A160209, A001652, A129857, A156035 (decimal expansion of 3+2*sqrt(2)), A160210 (decimal expansion of (1179+506*sqrt(2))/937), A160211 (decimal expansion of (933747+224782*sqrt(2))/937^2).
%K A129974 nonn,easy
%O A129974 1,2
%A A129974 _Mohamed Bouhamida_, Jun 13 2007
%E A129974 Edited and two terms added by _Klaus Brockhaus_, May 18 2009