A041897 Denominators of continued fraction convergents to sqrt(470).

1, 1, 3, 25, 53, 78, 3329, 3407, 10143, 84551, 179245, 263796, 11258677, 11522473, 34303623, 285951457, 606206537, 892157994, 38076842285, 38969000279, 116014842843, 967087743023, 2050190328889, 3017278071912, 128775869349193, 131793147421105

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, 0, 0, 3382, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -x^9 +3*x^8 -25*x^7 +53*x^6 -78*x^5 -53*x^4 -25*x^3 -3*x^2 -x -1) / (x^12 -3382*x^6 +1). - Colin Barker, Nov 27 2013

a(n) = 3382*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[470], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 3, 25, 53, 78, 3329, 3407, 10143, 84551, 179245, 263796]; [n le 12 select I[n] else 3382*Self(n-6)-Self(n-12): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041896, A040448.

Sequence in context: A145609 A259923 A120285 * A356594 A242974 A006222

Adjacent sequences: A041894 A041895 A041896 * A041898 A041899 A041900

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved