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Continued fraction for sqrt(113).
2

%I #44 Feb 07 2024 10:11:47

%S 10,1,1,1,2,2,1,1,1,20,1,1,1,2,2,1,1,1,20,1,1,1,2,2,1,1,1,20,1,1,1,2,

%T 2,1,1,1,20,1,1,1,2,2,1,1,1,20,1,1,1,2,2,1,1,1,20,1,1,1,2,2,1,1,1,20,

%U 1,1,1,2,2,1,1,1,20,1,1,1,2,2

%N Continued fraction for sqrt(113).

%H Vincenzo Librandi, <a href="/A010178/b010178.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).

%F G.f.: (10 + x + x^2 + x^3 + 2*x^4 + 2*x^5 + x^6 + x^7 + x^8 + 10*x^9)/(1-x^9). - _Vincenzo Librandi_, Jun 13 2013

%F a(n) = a(n-9), n >= 10. - _Vincenzo Librandi_, Jun 14 2013

%t ContinuedFraction[Sqrt[113], 300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 11 2011 *)

%t CoefficientList[Series[(10 + x + x^2 + x^3 + 2 x^4 + 2 x^5 + x^6 + x^7 + x^8 + 10 x^9) / (1 - x^9), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 13 2013 *)

%o (Magma) I:=[10, 1, 1, 1, 2, 2, 1, 1, 1, 20]; [n le 10 select I[n] else Self(n-9): n in [1..80]]; // _Vincenzo Librandi_, Jun 14 2013

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_