A041939 Denominators of continued fraction convergents to sqrt(492).

1, 5, 6, 11, 116, 127, 243, 1342, 59291, 297797, 357088, 654885, 6905938, 7560823, 14466761, 79894628, 3529830393, 17729046593, 21258876986, 38987923579, 411138112776, 450126036355, 861264149131, 4756446782010, 210144922557571, 1055481059569865

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, 59534, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -5*x^13 +6*x^12 -11*x^11 +116*x^10 -127*x^9 +243*x^8 -1342*x^7 -243*x^6 -127*x^5 -116*x^4 -11*x^3 -6*x^2 -5*x -1) / ((x^8 -244*x^4 +1)*(x^8 +244*x^4 +1)). - Colin Barker, Nov 27 2013

a(n) = 59534*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator/@Convergents[Sqrt[492], 40] (* Harvey P. Dale, Jun 22 2011 *)
CoefficientList[Series[-(x^14 - 5 x^13 + 6 x^12 - 11 x^11 + 116 x^10 - 127 x^9 + 243 x^8 - 1342 x^7 - 243 x^6 - 127 x^5 - 116 x^4 - 11 x^3 - 6 x^2 - 5 x - 1)/((x^8 - 244 x^4 + 1) (x^8 + 244 x^4 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)

Prog

(Magma) I:=[1, 5, 6, 11, 116, 127, 243, 1342, 59291, 297797, 357088, 654885, 6905938, 7560823, 14466761, 79894628]; [n le 16 select I[n] else 59534*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041938, A040469.

Sequence in context: A042183 A362020 A328544 * A177714 A273158 A099641

Adjacent sequences: A041936 A041937 A041938 * A041940 A041941 A041942

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved