A041087 Denominators of continued fraction convergents to sqrt(51).

1, 7, 99, 700, 9899, 69993, 989801, 6998600, 98970201, 699790007, 9896030299, 69972002100, 989504059699, 6996500419993, 98940509939601, 699580069997200, 9893061489900401, 69951010499300007, 989207208480100499, 6994401469860003500, 98910827786520149499

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,100,0,-1).

Formula

G.f.: -(x^2-7*x-1) / (x^4-100*x^2+1). - Colin Barker, Nov 12 2013

a(n) = 100*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[51], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
CoefficientList[Series[(1 + 7 x - x^2)/(x^4 - 100 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 7, 99, 700]; [n le 4 select I[n] else 100*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041086, A040043, A020808.

Sequence in context: A334722 A092818 A238472 * A041084 A115066 A340887

Adjacent sequences: A041084 A041085 A041086 * A041088 A041089 A041090

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved