A041787 Denominators of continued fraction convergents to sqrt(414).

1, 2, 3, 23, 49, 366, 415, 1196, 48255, 97706, 145961, 1119433, 2384827, 17813222, 20198049, 58209320, 2348570849, 4755351018, 7103921867, 54482804087, 116069530041, 866969514374, 983039044415, 2833047603204, 114304943172575, 231442933948354

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, 0, 0, 0, 0, 48670, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -2*x^13 +3*x^12 -23*x^11 +49*x^10 -366*x^9 +415*x^8 -1196*x^7 -415*x^6 -366*x^5 -49*x^4 -23*x^3 -3*x^2 -2*x -1) / (x^16 -48670*x^8 +1). - Colin Barker, Nov 24 2013

a(n) = 48670*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[414], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 2, 3, 23, 49, 366, 415, 1196, 48255, 97706, 145961, 1119433, 2384827, 17813222, 20198049, 58209320]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041786, A040393.

Sequence in context: A262838 A120366 A371310 * A143853 A195241 A090180

Adjacent sequences: A041784 A041785 A041786 * A041788 A041789 A041790

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 24 2013

Status

approved