A010178 Continued fraction for sqrt(113).

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, 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, 1, 1, 1, 2, 2, 1, 1, 1, 20, 1, 1, 1, 2, 2

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Formula

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

a(n) = a(n-9), n >= 10. - Vincenzo Librandi, Jun 14 2013

Mathematica

ContinuedFraction[Sqrt[113], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2011 *)
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 *)

Prog

(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

Crossrefs

Sequence in context: A284100 A279051 A332804 * A070596 A306363 A347119

Adjacent sequences: A010175 A010176 A010177 * A010179 A010180 A010181

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved