A041217 Denominators of continued fraction convergents to sqrt(119).

1, 1, 10, 11, 230, 241, 2399, 2640, 55199, 57839, 575750, 633589, 13247530, 13881119, 138177601, 152058720, 3179352001, 3331410721, 33162048490, 36493459211, 763031232710, 799524691921, 7958753459999, 8758278151920, 183124316498399, 191882594650319, 1910067668351270

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,240,0,0,0,-1).

Formula

G.f.: (1 +x +10*x^2 +11*x^3 -10*x^4 +x^5 -x^6)/(1 -240* x^4 +x^8). - Vincenzo Librandi, Dec 13 2013

a(n) = 240*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[119], 30]] (* or *) CoefficientList[Series[(1 + x + 10 x^2 + 11 x^3 - 10 x^4 + x^5 - x^6)/(1 - 240 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 240, 0, 0, 0, -1}, {1, 1, 10, 11, 230, 241, 2399, 2640}, 30] (* Harvey P. Dale, Jan 02 2020 *)

Prog

(Magma) I:=[1, 1, 10, 11, 230, 241, 2399, 2640]; [n le 8 select I[n] else 240*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041216.

Sequence in context: A361990 A335801 A363835 * A041218 A300458 A041917

Adjacent sequences: A041214 A041215 A041216 * A041218 A041219 A041220

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 13 2013

Status

approved