cp's OEIS Frontend

A207059 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+289)^2 = y^2.

%I A207059 #29 Feb 16 2025 08:33:16
%S A207059 119,231,300,476,867,1496,2120,2511,3519,5780,9435,13067,15344,21216,
%T A207059 34391,55692,76860,90131,124355,201144,325295,448671,526020,725492,
%U A207059 1173051,1896656,2615744,3066567,4229175,6837740,11055219,15246371,17873960,24650136
%N A207059 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+289)^2 = y^2.
%C A207059 For the generic case x^2 + (x + p^2)^2 = y^2 with p = 2*m^2 - 1 a prime number in A066436, m>=3, (0; p^2) and (4*m^3 + 2*m^2 - 2*m - 1; 4*m^4 + 4*m^3 - 2*m - 1) are solutions. - _Mohamed Bouhamida_, Aug 24 2019
%H A207059 Vincenzo Librandi, <a href="/A207059/b207059.txt">Table of n, a(n) for n = 1..1000</a>
%H A207059 Eric Weisstein, <a href="https://mathworld.wolfram.com/DiophantineEquation.html">Diophantine equation</a> (MathWorld).
%H A207059 Wikipedia, <a href="http://en.wikipedia.org/wiki/Diophantine_equation">Diophantine equation</a>
%H A207059 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,6,-6,0,0,0,-1,1).
%F A207059 G.f.: x*(85*x^9+48*x^8+23*x^7+48*x^6+85*x^5-391*x^4-176*x^3-69*x^2-112*x-119)/((x-1)*(x^10-6*x^5+1)). - _Colin Barker_, Aug 05 2012
%F A207059 a(n) = 6*a(n-5) - a(n-10) + 578 with a(1) = 119, a(2) = 231, a(3) = 300, a(4) = 476, a(5) = 867, a(6) = 1496, a(7) = 2120, a(8) = 2511, a(9) = 3519, a(10) = 5780. - _Mohamed Bouhamida_, Aug 24 2019
%t A207059 LinearRecurrence[ {1, 0, 0, 0, 6, -6, 0, 0, 0, -1, 1}, {119, 231, 300, 476, 867, 1496, 2120, 2511, 3519, 5780, 9435}, 60]
%o A207059 (PARI) Vec(x*(85*x^9+48*x^8+23*x^7+48*x^6+85*x^5-391*x^4-176*x^3-69*x^2-112*x-119)/((x-1)*(x^10-6*x^5+1))+O(x^60)) \\ _Stefano Spezia_, Aug 24 2019
%Y A207059 Cf. A204765, A205644, A205672, A207058.
%K A207059 nonn,easy
%O A207059 1,1
%A A207059 _Vladimir Joseph Stephan Orlovsky_, Feb 14 2012