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A041939 Denominators of continued fraction convergents to sqrt(492). 2
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 (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, 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: A041227 A042183 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

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Last modified December 15 15:01 EST 2019. Contains 329999 sequences. (Running on oeis4.)