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%I A175014 #32 Oct 11 2023 15:18:56
%S A175014 0,12,2136,380196,67672752,12045369660,2144008126728,381621401187924,
%T A175014 67926465403323744,12090529220390438508,2152046274764094730680,
%U A175014 383052146378788471622532,68181130009149583854080016
%N A175014 y-values in the solution to x^2-55*y^2=1.
%C A175014 The corresponding values of x of this Pell equation are in A174758.
%H A175014 Vincenzo Librandi, <a href="/A175014/b175014.txt">Table of n, a(n) for n = 1..200</a>
%H A175014 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (178,-1).
%F A175014 a(n) = 178*a(n-1)-a(n-2) with a(1)=0, a(2)=12.
%F A175014 G.f.: 12*x^2/(1-178*x+x^2).
%F A175014 a(n) = ((89+12*sqrt(55))^(n-1) - (89-12*sqrt(55))^(n-1))/(2*sqrt(55)). - _Alan Michael Gómez Calderón_, Oct 06 2023
%t A175014 LinearRecurrence[{178,-1},{0,12},30]
%o A175014 (Magma) I:=[0, 12]; [n le 2 select I[n] else 178*Self(n-1)-Self(n-2): n in [1..20]];
%Y A175014 Cf. A174758.
%K A175014 nonn,easy
%O A175014 1,2
%A A175014 _Vincenzo Librandi_, Apr 15 2010

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