A041137 Denominators of continued fraction convergents to sqrt(77).

1, 1, 4, 9, 31, 40, 671, 711, 2804, 6319, 21761, 28080, 471041, 499121, 1968404, 4435929, 15276191, 19712120, 330670111, 350382231, 1381816804, 3114015839, 10723864321, 13837880160, 232129946881, 245967827041, 970033428004, 2186034683049, 7528137477151

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,702,0,0,0,0,0,-1).

Formula

a(n) = 702*a(n-6)-a(n-12). G.f.: -(x^10-x^9+4*x^8-9*x^7+31*x^6-40*x^5-31*x^4-9*x^3-4*x^2-x-1)/((x^4-9*x^2+1)*(x^8+9*x^6+80*x^4+9*x^2+1)). [Colin Barker, Jul 18 2012]

Mathematica

Denominator/@Convergents[Sqrt[77], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[- (x^10 - x^9 + 4 x^8 - 9 x^7 + 31 x^6 - 40 x^5 - 31 x^4 - 9 x^3 - 4 x^2 - x - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)

Crossrefs

Cf. A010529, A041136.

Sequence in context: A230056 A069103 A364239 * A042599 A206960 A145543

Adjacent sequences: A041134 A041135 A041136 * A041138 A041139 A041140

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved