A041065 Denominators of continued fraction convergents to sqrt(39).

1, 4, 49, 200, 2449, 9996, 122401, 499600, 6117601, 24970004, 305757649, 1248000600, 15281764849, 62375059996, 763782484801, 3117504999200, 38173842475201, 155812874900004, 1907928341275249, 7787526240001000, 95358243221287249, 389220499125149996

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,50,0,-1).

Formula

G.f.: -(x^2-4*x-1) / (x^4-50*x^2+1). - Colin Barker, Nov 12 2013

a(n) = 50*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 10 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[39], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
Denominator[Convergents[Sqrt[39], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

Prog

(Magma) I:=[1, 4, 49, 200]; [n le 4 select I[n] else 50*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013

Crossrefs

Cf. A010493, A041064.

Sequence in context: A360883 A092866 A340662 * A166838 A166826 A295535

Adjacent sequences: A041062 A041063 A041064 * A041066 A041067 A041068

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved