A041827 Denominators of continued fraction convergents to sqrt(434).

1, 1, 5, 6, 245, 251, 1249, 1500, 61249, 62749, 312245, 374994, 15312005, 15686999, 78060001, 93747000, 3827940001, 3921687001, 19514688005, 23436375006, 956969688245, 980406063251, 4878593941249, 5859000004500, 239238594121249, 245097594125749

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,250,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+6*x^2+1) / (x^8-250*x^4+1). - Colin Barker, Nov 25 2013

a(n) = 250*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[434], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
LinearRecurrence[{0, 0, 0, 250, 0, 0, 0, -1}, {1, 1, 5, 6, 245, 251, 1249, 1500}, 30] (* Harvey P. Dale, Apr 27 2018 *)

Prog

(Magma) I:=[1, 1, 5, 6, 245, 251, 1249, 1500]; [n le 8 select I[n] else 250*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A041826, A040413.

Sequence in context: A103089 A041601 A301648 * A042089 A156191 A042387

Adjacent sequences: A041824 A041825 A041826 * A041828 A041829 A041830

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved