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Numerators of continued fraction convergents to sqrt(990).
2

%I #18 Jun 26 2022 23:30:51

%S 31,63,409,881,55031,110943,720689,1552321,96964591,195481503,

%T 1269853609,2735188721,170851554311,344438297343,2237481338369,

%U 4819400974081,301040341731391,606900084436863,3942440848352569,8491781781142001,530432911279156631

%N Numerators of continued fraction convergents to sqrt(990).

%H Vincenzo Librandi, <a href="/A042916/b042916.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1762,0,0,0,-1).

%F G.f.: (31 + 63*x + 409*x^2 + 881*x^3 +409*x^4 -63*x^5 +31*x^6 -x^7)/(1 -1762*x^4 +x^8). - _Vincenzo Librandi_, Dec 09 2013

%F a(n) = 1762*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 09 2013

%t Numerator[Convergents[Sqrt[990], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 409 x^2 + 881 x^3 + 409 x^4 - 63 x^5 + 31 x^6 - x^7)/(1 - 1762 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2013 *)

%t LinearRecurrence[{0,0,0,1762,0,0,0,-1},{31,63,409,881,55031,110943,720689,1552321},30] (* _Harvey P. Dale_, Jun 07 2020 *)

%o (Magma) I:=[31,63,409,881,55031,110943,720689,1552321]; [n le 8 select I[n] else 1762*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Dec 09 2013

%Y Cf. A042917.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 09 2013