A041716 Numerators of continued fraction convergents to sqrt(378).

19, 39, 136, 175, 836, 1011, 3869, 8749, 336331, 681411, 2380564, 3061975, 14628464, 17690439, 67699781, 153090001, 5885119819, 11923329639, 41655108736, 53578438375, 255968862236, 309547300611, 1184610764069, 2678768828749, 102977826256531, 208634421341811

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,17498,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -19*x^14 +39*x^13 -136*x^12 +175*x^11 -836*x^10 +1011*x^9 -3869*x^8 -8749*x^7 -3869*x^6 -1011*x^5 -836*x^4 -175*x^3 -136*x^2 -39*x -19) / (x^16 -17498*x^8 +1). - Colin Barker, Nov 11 2013

Mathematica

Numerator[Convergents[Sqrt[378], 30]] (* Vincenzo Librandi, Nov 07 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 17498, 0, 0, 0, 0, 0, 0, 0, -1}, {19, 39, 136, 175, 836, 1011, 3869, 8749, 336331, 681411, 2380564, 3061975, 14628464, 17690439, 67699781, 153090001}, 30] (* Harvey P. Dale, Jun 01 2022 *)

Crossrefs

Cf. A041717.

Sequence in context: A195048 A299964 A041714 * A041718 A041720 A098850

Adjacent sequences: A041713 A041714 A041715 * A041717 A041718 A041719

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 11 2013

Status

approved