%I #26 Apr 07 2024 14:39:12
%S 3,63,1383,30363,666603,14634903,321301263,7053992883,154866542163,
%T 3400009934703,74645352021303,1638797734533963,35978904807725883,
%U 789897108035435463,17341757471971854303,380728767275345359203
%N Numbers X such that 30*X^2-45 is a square.
%C Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 180 = 0. - _Colin Barker_, Feb 19 2014
%H Vincenzo Librandi, <a href="/A133275/b133275.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (22,-1).
%F a(n+2) = 22*a(n+1)-a(n).
%F a(n+1) = 11*a(n)+2*(30*a(n)^2-45)^0.5.
%F G.f.: -3*x*(-1+x)/(1-22*x+x^2). - _R. J. Mathar_, Nov 14 2007
%F a(n) = 3*A157014(n). - _Colin Barker_, Feb 19 2014
%t CoefficientList[Series[3 (1 - x)/(1 - 22 x + x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 21 2014 *)
%o (Magma) I:=[3,63]; [n le 2 select I[n] else 22*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Feb 21 2014
%Y Cf. A157014.
%K nonn,easy
%O 1,1
%A _Richard Choulet_, Oct 16 2007
%E More terms from _Paolo P. Lava_, Aug 06 2008