A041070 Numerators of continued fraction convergents to sqrt(42).

6, 13, 162, 337, 4206, 8749, 109194, 227137, 2834838, 5896813, 73596594, 153090001, 1910676606, 3974443213, 49603995162, 103182433537, 1287793197606, 2678768828749, 33433019142594, 69544807113937

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (0,26,0,-1).

Formula

G.f.: -(x+1)*(x^2-7*x-6) / (x^4-26*x^2+1). - Colin Barker, Nov 04 2013

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[42], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Numerator[Convergents[Sqrt[42], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 26, 0, -1}, {6, 13, 162, 337}, 30] (* Harvey P. Dale, Aug 07 2019 *)

Crossrefs

Cf. A041071, A010496.

Sequence in context: A336046 A368633 A042285 * A248263 A201449 A205300

Adjacent sequences: A041067 A041068 A041069 * A041071 A041072 A041073

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved