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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010544, A041167.

Programs

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 *)

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

Extensions

More terms from Colin Barker, Nov 10 2013