A041321 Denominators of continued fraction convergents to sqrt(174).

1, 5, 21, 110, 2881, 14515, 60941, 319220, 8360661, 42122525, 176850761, 926376330, 24262635341, 122239553035, 513220847481, 2688343790440, 70410159398921, 354739140785045, 1489366722539101, 7801572753480550, 204330258313033401, 1029452864318647555

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2902,0,0,0,-1).

Formula

G.f.: -(x^2-5*x-1)*(x^4+22*x^2+1) / (x^8-2902*x^4+1). - Colin Barker, Nov 15 2013

a(n) = 2902*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[174], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 2902, 0, 0, 0, -1}, {1, 5, 21, 110, 2881, 14515, 60941, 319220}, 30] (* Harvey P. Dale, Jun 21 2022 *)

Prog

(Magma) I:=[1, 5, 21, 110, 2881, 14515, 60941, 319220]; [n le 8 select I[n] else 2902*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041320, A010218.

Sequence in context: A325157 A218299 A121881 * A082428 A015558 A168598

Adjacent sequences: A041318 A041319 A041320 * A041322 A041323 A041324

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved