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A176368 x-values in the solution to x^2 - 65*y^2 = 1.

%I A176368 #16 Sep 08 2022 08:45:52
%S A176368 1,129,33281,8586369,2215249921,571525893249,147451465208321,
%T A176368 38041906497853569,9814664424981012481,2532145379738603366529,
%U A176368 653283693308134687552001,168544660728119010785049729
%N A176368 x-values in the solution to x^2 - 65*y^2 = 1.
%C A176368 The corresponding values of y of this Pell equation are in A176369.
%H A176368 Vincenzo Librandi, <a href="/A176368/b176368.txt">Table of n, a(n) for n = 1..200</a>
%H A176368 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (258,-1).
%F A176368 a(n) = 258*a(n-1) - a(n-2) with a(1)=1, a(2)=129.
%F A176368 G.f.: x*(1-129*x)/(1-258*x+x^2).
%p A176368 seq(coeff(series(x*(1-129*x)/(1-258*x+x^2), x, n+1), x, n), n = 1..15); # _G. C. Greubel_, Dec 08 2019
%t A176368 LinearRecurrence[{258,-1},{1,129},30]
%o A176368 (Magma) I:=[1, 129]; [n le 2 select I[n] else 258*Self(n-1)-Self(n-2): n in [1..20]];
%o A176368 (PARI) my(x='x+O('x^15)); Vec(x*(1-129*x)/(1-258*x+x^2)) \\ _G. C. Greubel_, Dec 08 2019
%o A176368 (Sage)
%o A176368 def A176368_list(prec):
%o A176368     P.<x> = PowerSeriesRing(ZZ, prec)
%o A176368     return P( x*(1-129*x)/(1-258*x+x^2) ).list()
%o A176368 a=A176368_list(15); a[1:] # _G. C. Greubel_, Dec 08 2019
%o A176368 (GAP) a:=[1,129];; for n in [3..15] do a[n]:=258*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Dec 08 2019
%Y A176368 Cf. A176369, Row 8 of array A188645.
%K A176368 nonn,easy
%O A176368 1,2
%A A176368 _Vincenzo Librandi_, Apr 16 2010