A041124 Numerators of continued fraction convergents to sqrt(71).

8, 17, 42, 59, 455, 514, 1483, 3480, 57163, 117806, 292775, 410581, 3166842, 3577423, 10321688, 24220799, 397854472, 819929743, 2037713958, 2857643701, 22041219865, 24898863566, 71838946997, 168576757560, 2769067067957, 5706710893474, 14182488854905

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -8*x^14 +17*x^13 -42*x^12 +59*x^11 -455*x^10 +514*x^9 -1483*x^8 -3480*x^7 -1483*x^6 -514*x^5 -455*x^4 -59*x^3 -42*x^2 -17*x -8) / (x^16 -6960*x^8 +1). - Colin Barker, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[71], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 6960, 0, 0, 0, 0, 0, 0, 0, -1}, {8, 17, 42, 59, 455, 514, 1483, 3480, 57163, 117806, 292775, 410581, 3166842, 3577423, 10321688, 24220799}, 40] (* Harvey P. Dale, Aug 14 2023 *)

Crossrefs

Cf. A010523, A041125.

Sequence in context: A297728 A188129 A041849 * A048695 A329768 A153873

Adjacent sequences: A041121 A041122 A041123 * A041125 A041126 A041127

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 05 2013

Status

approved