A042203 Denominators of continued fraction convergents to sqrt(627).

1, 25, 1251, 31300, 1566251, 39187575, 1960945001, 49062812600, 2455101575001, 61426602187625, 3073785210956251, 76906056876093900, 3848376629015651251, 96286321782267375175, 4818164465742384410001, 120550397965341877625200, 6032338062732836265670001

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1252,0,-1).

Formula

G.f.: -(x^2 - 25*x - 1) / (x^4 - 1252*x^2 + 1). - Colin Barker, Dec 04 2013

a(n) = 1252*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Jan 16 2014

Mathematica

Denominator[Convergents[Sqrt[627], 30]] (* Vincenzo Librandi, Jan 16 2014 *)
LinearRecurrence[{0, 1252, 0, -1}, {1, 25, 1251, 31300}, 20] (* Harvey P. Dale, Dec 28 2024 *)

Prog

(Magma) I:=[1, 25, 1251, 31300]; [n le 4 select I[n] else 1252*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 16 2014

Crossrefs

Cf. A042202, A040601.

Sequence in context: A181719 A096330 A174751 * A042200 A104593 A046910

Adjacent sequences: A042200 A042201 A042202 * A042204 A042205 A042206

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 04 2013

Status

approved