A041174 Numerators of continued fraction convergents to sqrt(97).

9, 10, 59, 69, 128, 197, 325, 522, 847, 4757, 5604, 105629, 111233, 661794, 773027, 1434821, 2207848, 3642669, 5850517, 9493186, 53316447, 62809633, 1183889841, 1246699474, 7417387211, 8664086685, 16081473896, 24745560581, 40827034477, 65572595058

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 (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A010548, A041175, A010168, A020854.

Programs

Mathematica

Numerator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Oct 30 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1},{9,10,59,69,128,197,325,522,847,4757,5604,105629,111233,661794,773027,1434821,2207848,3642669,5850517,9493186,53316447,62809633},30] (* Harvey P. Dale, Aug 02 2021 *)

Formula

G.f.: -(x^21 -9*x^20 +10*x^19 -59*x^18 +69*x^17 -128*x^16 +197*x^15 -325*x^14 +522*x^13 -847*x^12 +4757*x^11 +5604*x^10 +4757*x^9 +847*x^8 +522*x^7 +325*x^6 +197*x^5 +128*x^4 +69*x^3 +59*x^2 +10*x +9) / (x^22 +11208*x^11 -1). - Colin Barker, Nov 14 2013

Extensions

More terms from Colin Barker, Nov 14 2013