cp's OEIS Frontend

A130610 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+359)^2 = y^2.

%I A130610 #9 Feb 15 2020 10:52:27
%S A130610 0,40,901,1077,1281,6160,7180,8364,36777,42721,49621,215220,249864,
%T A130610 290080,1255261,1457181,1691577,7317064,8493940,9860100,42647841,
%U A130610 49507177,57469741,248570700,288549840,334959064,1448777077,1681792581
%N A130610 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+359)^2 = y^2.
%C A130610 Also values x of Pythagorean triples (x, x+359, y).
%C A130610 Corresponding values y of solutions (x, y) are in A159844.
%C A130610 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 A130610 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A130610 lim_{n -> infinity} a(n)/a(n-1) = (363+38*sqrt(2))/359 for n mod 3 = {1, 2}.
%C A130610 lim_{n -> infinity} a(n)/a(n-1) = (293619+186550*sqrt(2))/359^2 for n mod 3 = 0.
%H A130610 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
%F A130610 a(n) = 6*a(n-3)-a(n-6)+718 for n > 6; a(1)=0, a(2)=40, a(3)=901, a(4)=1077, a(5)=1281, a(6)=6160.
%F A130610 G.f.: x*(40+861*x+176*x^2-36*x^3-287*x^4-36*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F A130610 a(3*k+1) = 359*A001652(k) for k >= 0.
%o A130610 (PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+718*n+128881), print1(n, ",")))}
%Y A130610 Cf. A159844, A028871, A118337, A130609, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159845 (decimal expansion of (363+38*sqrt(2))/359), A159846 (decimal expansion of (293619+186550*sqrt(2))/359^2).
%K A130610 nonn,easy
%O A130610 1,2
%A A130610 _Mohamed Bouhamida_, Jun 17 2007
%E A130610 Edited and two terms added by _Klaus Brockhaus_, Apr 30 2009