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A041378 Numerators of continued fraction convergents to sqrt(204). 2
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 07 2013

STATUS

approved

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Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)