cp's OEIS Frontend

A161478 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+113)^2 = y^2.

%I A161478 #8 Jul 31 2015 22:13:52
%S A161478 0,52,175,339,615,1312,2260,3864,7923,13447,22795,46452,78648,133132,
%T A161478 271015,458667,776223,1579864,2673580,4524432,9208395,15583039,
%U A161478 26370595,53670732,90824880,153699364,312816223,529366467,895825815,1823226832,3085374148
%N A161478 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+113)^2 = y^2.
%C A161478 Corresponding values y of solutions (x, y) are in A161479.
%C A161478 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A161478 lim_{n -> infinity} a(n)/a(n-1) = (129+44*sqrt(2))/113 for n mod 3 = {1, 2}.
%C A161478 lim_{n -> infinity} a(n)/a(n-1) = (16131+6970*sqrt(2))/113^2 for n mod 3 = 0.
%H A161478 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 6, -6, 0, -1, 1).
%F A161478 a(n) = 6*a(n-3)-a(n-6)+226 for n > 6; a(1)=0, a(2)=52, a(3)=175, a(4)=339, a(5)=615, a(6)=1312.
%F A161478 G.f.: x*(52+123*x+164*x^2-36*x^3-41*x^4-36*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F A161478 a(3*k+1) = 113*A001652(k) for k >= 0.
%t A161478 LinearRecurrence[{1,0,6,-6,0,-1,1},{0,52,175,339,615,1312,2260},72] (* _Vladimir Joseph Stephan Orlovsky_, Feb 07 2012 *)
%o A161478 (PARI) {forstep(n=0, 100000000, [3, 1], if(issquare(2*n^2+226*n+12769), print1(n, ",")))}
%Y A161478 Cf. A161479, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A161480 (decimal expansion of (129+44*sqrt(2))/113), A161481 (decimal expansion of (16131+6970*sqrt(2))/113^2).
%K A161478 nonn
%O A161478 1,2
%A A161478 _Klaus Brockhaus_, Jun 13 2009