A041414 Numerators of continued fraction convergents to sqrt(222).

14, 15, 134, 149, 4306, 4455, 39946, 44401, 1283174, 1327575, 11903774, 13231349, 382381546, 395612895, 3547284706, 3942897601, 113948417534, 117891315135, 1057078938614, 1174970253749, 33956246043586

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,298,0,0,0,-1).

Formula

G.f.: (14 +15*x +134*x^2 +149*x^3 +134*x^4 -15*x^5 +14*x^6 -x^7) / (1 -298*x^4 +x^8). - Vincenzo Librandi, Nov 02 2013

Mathematica

Numerator[Convergents[Sqrt[222], 30]] (* or *) CoefficientList[Series[(14 + 15 x + 134 x^2 + 149 x^3 + 134 x^4 - 15 x^5 + 14 x^6 - x^7)/(1 - 298 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 02 2013 *)
LinearRecurrence[{0, 0, 0, 298, 0, 0, 0, -1}, {14, 15, 134, 149, 4306, 4455, 39946, 44401}, 40] (* Harvey P. Dale, Dec 02 2024 *)

Crossrefs

Cf. A041415.

Sequence in context: A041410 A372335 A041412 * A033050 A225757 A041416

Adjacent sequences: A041411 A041412 A041413 * A041415 A041416 A041417

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved