A041146 Numerators of continued fraction convergents to sqrt(83).

9, 82, 1485, 13447, 243531, 2205226, 39937599, 361643617, 6549522705, 59307347962, 1074081786021, 9726043422151, 176142863384739, 1595011813884802, 28886355513311175, 261572211433685377, 4737186161319647961, 42896247663310517026, 776869644100908954429

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..70

Index entries for linear recurrences with constant coefficients, signature (0,164,0,-1).

Formula

G.f.: -(x^3-9*x^2-82*x-9) / (x^4-164*x^2+1). - Colin Barker, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[83], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 164, 0, -1}, {9, 82, 1485, 13447}, 20] (* Harvey P. Dale, Apr 12 2022 *)

Crossrefs

Cf. A010534, A041147.

Sequence in context: A338663 A308668 A308481 * A320991 A015497 A174472

Adjacent sequences: A041143 A041144 A041145 * A041147 A041148 A041149

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 05 2013

Status

approved