A199338 - OEIS

%I #28 Sep 08 2022 08:46:00

%S 1,11,19,89,151,701,1189,5519,9361,43451,73699,342089,580231,2693261,

%T 4568149,21203999,35964961,166938731,283151539,1314305849,2229247351,

%U 10347508061,17550827269,81465758639,138177370801,641378561051,1087868139139,5049562729769

%N y-values in the solution to 15*x^2 - 14 = y^2.

%C When are both n+1 and 15*n+1 perfect squares? This problem gives the equation 15*x^2-14=y^2.

%C Essentially the same as A103201. - _R. J. Mathar_, Nov 11 2011

%H Vincenzo Librandi, <a href="/A199338/b199338.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).

%F a(n+4) = 8*a(n+2) - a(n) with a(1)=1, a(2)=11, a(3)=19, a(4)=89.

%F G.f.: x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4). - _Bruno Berselli_, Nov 08 2011

%t LinearRecurrence[{0, 8, 0, -1}, {1, 11, 19, 89}, 50]

%o (Magma) m:=29; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4))); // _Bruno Berselli_, Nov 08 2011

%Y Cf. A199336.

%K nonn,easy

%O 1,2

%A _Sture Sjöstedt_, Nov 08 2011