A042816 Numerators of continued fraction convergents to sqrt(939).

30, 31, 61, 92, 429, 8672, 35117, 43789, 78906, 122695, 7440606, 7563301, 15003907, 22567208, 105272739, 2128021988, 8617360691, 10745382679, 19362743370, 30108126049, 1825850306310, 1855958432359, 3681808738669, 5537767171028

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, 0, 0, 245390, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^19 -30*x^18 +31*x^17 -61*x^16 +92*x^15 -429*x^14 +8672*x^13 -35117*x^12 +43789*x^11 -78906*x^10 -122695*x^9 -78906*x^8 -43789*x^7 -35117*x^6 -8672*x^5 -429*x^4 -92*x^3 -61*x^2 -31*x -30) / (x^20 -245390*x^10 +1). - Colin Barker, Dec 24 2013

Mathematica

Numerator[Convergents[Sqrt[939], 30]] (* Vincenzo Librandi, Dec 05 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 245390, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {30, 31, 61, 92, 429, 8672, 35117, 43789, 78906, 122695, 7440606, 7563301, 15003907, 22567208, 105272739, 2128021988, 8617360691, 10745382679, 19362743370, 30108126049}, 30] (* Harvey P. Dale, Oct 08 2023 *)

Crossrefs

Cf. A042817, A040908.

Sequence in context: A022400 A042812 A042814 * A042818 A042808 A042810

Adjacent sequences: A042813 A042814 A042815 * A042817 A042818 A042819

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 24 2013

Status

approved