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

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).

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

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 *)

Crossrefs

Cf. A010548, A041175, A010168, A020854.

Sequence in context: A368047 A037954 A271062 * A048070 A341527 A167708

Adjacent sequences: A041171 A041172 A041173 * A041175 A041176 A041177

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved