A041034 Numerators of continued fraction convergents to sqrt(22).

4, 5, 14, 61, 136, 197, 1712, 1909, 5530, 24029, 53588, 77617, 674524, 752141, 2178806, 9467365, 21113536, 30580901, 265760744, 296341645, 858444034, 3730117781, 8318679596, 12048797377, 104709058612

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,394,0,0,0,0,0,-1).

Formula

a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +5*x^9 -14*x^8 +61*x^7 -136*x^6 -197*x^5 -136*x^4 -61*x^3 -14*x^2 -5*x -4)/(x^12-394*x^6+1). [Colin Barker, Jul 16 2012]

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[22], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^11 - 4 x^10 + 5 x^9 - 14 x^8 + 61 x^7 - 136 x^6 - 197 x^5 - 136 x^4 - 61 x^3 - 14 x^2 - 5 x - 4)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1}, {4, 5, 14, 61, 136, 197, 1712, 1909, 5530, 24029, 53588, 77617}, 30] (* Harvey P. Dale, Mar 14 2017 *)

Crossrefs

Cf. A010478, A041035.

Sequence in context: A352683 A182252 A041857 * A281911 A042535 A222489

Adjacent sequences: A041031 A041032 A041033 * A041035 A041036 A041037

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved