A041235 Denominators of continued fraction convergents to sqrt(129).

1, 2, 3, 11, 14, 95, 109, 422, 531, 1484, 33179, 67842, 101021, 370905, 471926, 3202461, 3674387, 14225622, 17900009, 50025640, 1118464089, 2286953818, 3405417907, 12503207539, 15908625446, 107954960215, 123863585661, 479545717198, 603409302859

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,33710,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -2*x^17 +3*x^16 -11*x^15 +14*x^14 -95*x^13 +109*x^12 -422*x^11 +531*x^10 -1484*x^9 -531*x^8 -422*x^7 -109*x^6 -95*x^5 -14*x^4 -11*x^3 -3*x^2 -2*x -1) / (x^20 -33710*x^10 +1). - Colin Barker, Nov 14 2013

a(n) = 33710*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[129], 30]] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 33710, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 11, 14, 95, 109, 422, 531, 1484, 33179, 67842, 101021, 370905, 471926, 3202461, 3674387, 14225622, 17900009, 50025640}, 30] (* Harvey P. Dale, Nov 05 2020 *)

Prog

(Magma) I:=[1, 2, 3, 11, 14, 95, 109, 422, 531, 1484, 33179, 67842, 101021, 370905, 471926, 3202461, 3674387, 14225622, 17900009, 50025640]; [n le 20 select I[n] else 33710*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041234, A010190.

Sequence in context: A041029 A158353 A158355 * A036972 A041637 A042235

Adjacent sequences: A041232 A041233 A041234 * A041236 A041237 A041238

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved