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A041117 Denominators of continued fraction convergents to sqrt(67). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 11:17 EDT 2021. Contains 345375 sequences. (Running on oeis4.)