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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010529, A041136.

Programs

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 *)

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]