# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a200409 Showing 1-1 of 1 %I A200409 #24 May 06 2024 06:55:05 %S A200409 1,39,571,911,13299,194141,309739,4521621,66007369,105310349, %T A200409 1537337841,22442311319,35805208921,522690344319,7630319841091, %U A200409 12173665722791,177713179730619,2594286303659621,4139010540540019,60421958418066141,882049712924430049 %N A200409 The y-values in the solution to 19*x^2 - 18 = y^2. %C A200409 When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2 - 18 = y^2. %H A200409 Vincenzo Librandi, Table of n, a(n) for n = 1..300 %H A200409 Index entries for linear recurrences with constant coefficients, signature (0,0,340,0,0,-1). %F A200409 a(n) = 340*a(n-3) - a(n-6), a(1)=1, a(2)=39, a(3)=571, a(4)=911, a(5)=13299, a(6)=194141. %F A200409 G.f.: x*(x+1)*(x^4 + 38*x^3 + 533*x^2 + 38*x + 1) / (x^6 - 340*x^3 + 1). - _Colin Barker_, Sep 01 2013 %e A200409 a(7) = 340*911 - 1 = 309739. %t A200409 LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 39, 571, 911, 13299,194141}, 50] %o A200409 (Magma) I:=[1, 39, 571, 911, 13299, 194141]; [n le 6 select I[n] else 340*Self(n-3)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2011 %o A200409 (PARI) Vec(x*(x+1)*(x^4+38*x^3+533*x^2+38*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ _Colin Barker_, Sep 01 2013 %Y A200409 Cf. A200407, A199773, A199774, A199798. %K A200409 nonn,easy %O A200409 1,2 %A A200409 _Sture Sjöstedt_, Nov 17 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE