A041378 Numerators of continued fraction convergents to sqrt(204).

14, 43, 57, 100, 657, 757, 1414, 4999, 141386, 429157, 570543, 999700, 6568743, 7568443, 14137186, 49980001, 1413577214, 4290711643, 5704288857, 9995000500, 65674291857, 75669292357, 141343584214, 499700044999, 14132944844186, 42898534577557, 57031479421743

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -14*x^14 +43*x^13 -57*x^12 +100*x^11 -657*x^10 +757*x^9 -1414*x^8 -4999*x^7 -1414*x^6 -757*x^5 -657*x^4 -100*x^3 -57*x^2 -43*x -14) / ((x^8 -100*x^4 +1)*(x^8 +100*x^4 +1)). - Colin Barker, Nov 07 2013

Mathematica

Numerator[Convergents[Sqrt[204], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 9998, 0, 0, 0, 0, 0, 0, 0, -1}, {14, 43, 57, 100, 657, 757, 1414, 4999, 141386, 429157, 570543, 999700, 6568743, 7568443, 14137186, 49980001}, 30] (* Harvey P. Dale, Oct 03 2022 *)

Crossrefs

Cf. A041379.

Sequence in context: A292051 A242897 A120714 * A302219 A302665 A041380

Adjacent sequences: A041375 A041376 A041377 * A041379 A041380 A041381

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 07 2013

Status

approved