A041382 Numerators of continued fraction convergents to sqrt(206).

14, 29, 43, 244, 3459, 17539, 20998, 59535, 1687978, 3435491, 5123469, 29052836, 411863173, 2088368701, 2500231874, 7088832449, 200987540446, 409063913341, 610051453787, 3459321182276, 49040548005651, 248662061210531, 297702609216182, 844067279642895

Offset

0,1

Links

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

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

Formula

G.f.: -(x^15 -14*x^14 +29*x^13 -43*x^12 +244*x^11 -3459*x^10 +17539*x^9 -20998*x^8 -59535*x^7 -20998*x^6 -17539*x^5 -3459*x^4 -244*x^3 -43*x^2 -29*x -14) / (x^16 -119070*x^8 +1). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[206], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 119070, 0, 0, 0, 0, 0, 0, 0, -1}, {14, 29, 43, 244, 3459, 17539, 20998, 59535, 1687978, 3435491, 5123469, 29052836, 411863173, 2088368701, 2500231874, 7088832449}, 30] (* Harvey P. Dale, Jan 01 2026 *)

Crossrefs

Cf. A041383.

Sequence in context: A353197 A306212 A041384 * A047725 A257645 A046045

Adjacent sequences: A041379 A041380 A041381 * A041383 A041384 A041385

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved