A041166 Numerators of continued fraction convergents to sqrt(93).

9, 10, 19, 29, 135, 839, 3491, 4330, 7821, 12151, 226539, 238690, 465229, 703919, 3280905, 20389349, 84838301, 105227650, 190065951, 295293601, 5505350769, 5800644370, 11305995139, 17106639509, 79732553175, 495501958559, 2061740387411, 2557242345970

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,24302,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -9*x^18 +10*x^17 -19*x^16 +29*x^15 -135*x^14 +839*x^13 -3491*x^12 +4330*x^11 -7821*x^10 -12151*x^9 -7821*x^8 -4330*x^7 -3491*x^6 -839*x^5 -135*x^4 -29*x^3 -19*x^2 -10*x -9) / (x^20 -24302*x^10 +1). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[93], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 24302, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {9, 10, 19, 29, 135, 839, 3491, 4330, 7821, 12151, 226539, 238690, 465229, 703919, 3280905, 20389349, 84838301, 105227650, 190065951, 295293601}, 30] (* Harvey P. Dale, Apr 10 2023 *)

Crossrefs

Cf. A010544, A041167.

Sequence in context: A050551 A022099 A042113 * A042613 A020694 A042095

Adjacent sequences: A041163 A041164 A041165 * A041167 A041168 A041169

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved