cp's OEIS Frontend

A130014 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+881)^2 = y^2.

%I A130014 #12 Feb 15 2020 10:52:27
%S A130014 0,43,2440,2643,2860,16443,17620,18879,97980,104839,112176,573199,
%T A130014 613176,655939,3342976,3575979,3825220,19486419,20844460,22297143,
%U A130014 113577300,121492543,129959400,661979143,708112560,757461019,3858299320
%N A130014 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+881)^2 = y^2.
%C A130014 Also values x of Pythagorean triples (x, x+881, y).
%C A130014 Corresponding values y of solutions (x, y) are in A159690.
%C A130014 For the generic case x^2+(x+p)^2 = y^2 with p = 2*m^2-1 a (prime) number in A066436 see A118673 or A129836.
%C A130014 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A130014 lim_{n -> infinity} a(n)/a(n-1) = (883+42*sqrt(2))/881 for n mod 3 = {1, 2}.
%C A130014 lim_{n -> infinity} a(n)/a(n-1) = (2052963+1343918*sqrt(2))/881^2 for n mod 3 = 0.
%H A130014 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
%F A130014 a(n) = 6*a(n-3)-a(n-6)+1762 for n > 6; a(1)=0, a(2)=43, a(3)=2440, a(4)=2643, a(5)=2860, a(6)=16443.
%F A130014 G.f.: x*(43+2397*x+203*x^2-41*x^3-799*x^4-41*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F A130014 a(3*k+1) = 881*A001652(k) for k >= 0.
%t A130014 LinearRecurrence[{1,0,6,-6,0,-1,1},{0,43,2440,2643,2860,16443,17620},30] (* _Harvey P. Dale_, Aug 13 2015 *)
%o A130014 (PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+1762*n+776161), print1(n, ",")))}
%Y A130014 Cf. A159690, A066436, A118673, A118674, A129836, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159691 (decimal expansion of (883+42*sqrt(2))/881), A159692 (decimal expansion of (2052963+1343918*sqrt(2))/881^2).
%K A130014 nonn,easy
%O A130014 1,2
%A A130014 _Mohamed Bouhamida_, Jun 15 2007
%E A130014 Edited and two terms added by _Klaus Brockhaus_, Apr 21 2009