A041383 Denominators of continued fraction convergents to sqrt(206).

1, 2, 3, 17, 241, 1222, 1463, 4148, 117607, 239362, 356969, 2024207, 28695867, 145503542, 174199409, 493902360, 14003465489, 28500833338, 42504298827, 241022327473, 3416816883449, 17325106744718, 20741923628167, 58808954001052, 1667392635657623

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,119070,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +3*x^12 -17*x^11 +241*x^10 -1222*x^9 +1463*x^8 -4148*x^7 -1463*x^6 -1222*x^5 -241*x^4 -17*x^3 -3*x^2 -2*x -1) / (x^16 -119070*x^8 +1). - Colin Barker, Nov 16 2013

a(n) = 119070*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[206], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 2, 3, 17, 241, 1222, 1463, 4148, 117607, 239362, 356969, 2024207, 28695867, 145503542, 174199409, 493902360]; [n le 16 select I[n] else 119070*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041382, A040191.

Sequence in context: A328340 A042978 A089675 * A042903 A367686 A132534

Adjacent sequences: A041380 A041381 A041382 * A041384 A041385 A041386

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved