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A175014 y-values in the solution to x^2-55*y^2=1. 2

%I #32 Oct 11 2023 15:18:56

%S 0,12,2136,380196,67672752,12045369660,2144008126728,381621401187924,

%T 67926465403323744,12090529220390438508,2152046274764094730680,

%U 383052146378788471622532,68181130009149583854080016

%N y-values in the solution to x^2-55*y^2=1.

%C The corresponding values of x of this Pell equation are in A174758.

%H Vincenzo Librandi, <a href="/A175014/b175014.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 (178,-1).

%F a(n) = 178*a(n-1)-a(n-2) with a(1)=0, a(2)=12.

%F G.f.: 12*x^2/(1-178*x+x^2).

%F 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 LinearRecurrence[{178,-1},{0,12},30]

%o (Magma) I:=[0, 12]; [n le 2 select I[n] else 178*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174758.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 15 2010

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)