A041345 Denominators of continued fraction convergents to sqrt(186).

1, 1, 2, 3, 11, 47, 152, 199, 351, 550, 14651, 15201, 29852, 45053, 165011, 705097, 2280302, 2985399, 5265701, 8251100, 219794301, 228045401, 447839702, 675885103, 2475495011, 10577865147, 34209090452, 44786955599, 78996046051, 123783001650

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,15002,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +11*x^14 -47*x^13 +152*x^12 -199*x^11 +351*x^10 -550*x^9 -351*x^8 -199*x^7 -152*x^6 -47*x^5 -11*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -15002*x^10 +1). - Colin Barker, Nov 15 2013

a(n) = 15002*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[186], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 11, 47, 152, 199, 351, 550, 14651, 15201, 29852, 45053, 165011, 705097, 2280302, 2985399, 5265701, 8251100]; [n le 20 select I[n] else 15002*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041344, A010228.

Sequence in context: A128455 A260159 A287060 * A268285 A100701 A011365

Adjacent sequences: A041342 A041343 A041344 * A041346 A041347 A041348

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved