A041598 Numerators of continued fraction convergents to sqrt(317).

17, 18, 89, 730, 819, 2368, 5555, 7923, 68939, 283679, 352618, 12272691, 12625309, 62773927, 514816725, 577590652, 1669998029, 3917586710, 5587584739, 48618264622, 200060643227, 248678907849, 8655143510093, 8903822417942, 44270433181861, 363067287872830

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,705236,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^21 -17*x^20 +18*x^19 -89*x^18 +730*x^17 -819*x^16 +2368*x^15 -5555*x^14 +7923*x^13 -68939*x^12 +283679*x^11 +352618*x^10 +283679*x^9 +68939*x^8 +7923*x^7 +5555*x^6 +2368*x^5 +819*x^4 +730*x^3 +89*x^2 +18*x +17) / (x^22 +705236*x^11 -1). - Colin Barker, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[317], 30]] (* Vincenzo Librandi, Nov 04 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 705236, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {17, 18, 89, 730, 819, 2368, 5555, 7923, 68939, 283679, 352618, 12272691, 12625309, 62773927, 514816725, 577590652, 1669998029, 3917586710, 5587584739, 48618264622, 200060643227, 248678907849}, 30] (* Harvey P. Dale, May 24 2015 *)

Crossrefs

Cf. A041599, A040299.

Sequence in context: A041596 A041600 A341113 * A344138 A041602 A041604

Adjacent sequences: A041595 A041596 A041597 * A041599 A041600 A041601

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved