A176369 - OEIS

%I #29 Sep 08 2022 08:45:52

%S 0,16,4128,1065008,274767936,70889062480,18289103351904,

%T 4718517775728752,1217359297034666112,314073980117168128144,

%U 81029869510932342395040,20905392259840427169792176

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

%C The corresponding values of x of this Pell equation are in A176368.

%H Vincenzo Librandi, <a href="/A176369/b176369.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 (258,-1).

%F a(n) = 258*a(n-1) - a(n-2) with a(0)=0, a(1)=16.

%F G.f.: 16*x^2/(1-258*x+x^2).

%p seq(coeff(series(16*x^2/(1-258*x+x^2), x, n+1), x, n), n = 1..15); # _G. C. Greubel_, Dec 08 2019

%t LinearRecurrence[{258,-1},{0,16},20] (* _Harvey P. Dale_, Aug 20 2011 *)

%o (Magma) I:=[0,16]; [n le 2 select I[n] else 258*Self(n-1)-Self(n-2): n in [1..20]];

%o (PARI) my(x='x+O('x^15)); concat([0], Vec(16*x^2/(1-258*x+x^2))) \\ _G. C. Greubel_, Dec 08 2019

%o (Sage)

%o def A176369_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( 16*x^2/(1-258*x+x^2) ).list()

%o a=A176369_list(15); a[1:] # _G. C. Greubel_, Dec 08 2019

%o (GAP) a:=[1,16];; for n in [3..15] do a[n]:=258*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Dec 08 2019

%Y Cf. A176368.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 16 2010

%E Partially corrected and edited by _Michael B. Porter_ and _N. J. A. Sloane_, Jun 22 2010