A041117 Denominators of continued fraction convergents to sqrt(67).

1, 5, 11, 16, 27, 205, 232, 437, 1106, 5967, 96578, 488857, 1074292, 1563149, 2637441, 20025236, 22662677, 42687913, 108038503, 582880428, 9434125351, 47753507183, 104941139717, 152694646900, 257635786617, 1956145153219, 2213780939836, 4169926093055

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,97684,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -5*x^17 +11*x^16 -16*x^15 +27*x^14 -205*x^13 +232*x^12 -437*x^11 +1106*x^10 -5967*x^9 -1106*x^8 -437*x^7 -232*x^6 -205*x^5 -27*x^4 -16*x^3 -11*x^2 -5*x -1) / (x^20 -97684*x^10 +1). - Colin Barker, Nov 13 2013

a(n) = 97684*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[67], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[67], 30]] (* Harvey P. Dale, Oct 03 2012 *)
CoefficientList[Series[-(x^18 - 5 x^17 + 11 x^16 - 16 x^15 + 27 x^14 - 205 x^13 + 232 x^12 - 437 x^11 + 1106 x^10 - 5967 x^9 - 1106 x^8 - 437 x^7 - 232 x^6 - 205 x^5 - 27 x^4 - 16 x^3 - 11 x^2 - 5 x - 1)/(x^20 - 97684 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 5, 11, 16, 27, 205, 232, 437, 1106, 5967, 96578, 488857, 1074292, 1563149, 2637441, 20025236, 22662677, 42687913, 108038503, 582880428]; [n le 20 select I[n] else 97684*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041116, A010147, A020824, A010519.

Sequence in context: A022136 A042385 A041046 * A041491 A058025 A042121

Adjacent sequences: A041114 A041115 A041116 * A041118 A041119 A041120

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 13 2013

Status

approved