A041098 Numerators of continued fraction convergents to sqrt(57).

7, 8, 15, 68, 83, 151, 2197, 2348, 4545, 20528, 25073, 45601, 663487, 709088, 1372575, 6199388, 7571963, 13771351, 200370877, 214142228, 414513105, 1872194648, 2286707753, 4158902401, 60511341367

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,302,0,0,0,0,0,-1).

Formula

a(n) = 302*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-15*x^8+68*x^7-83*x^6-151*x^5-83*x^4-68*x^3-15*x^2-8*x-7)/(x^12-302*x^6+1). [Colin Barker, Jul 18 2012]

Mathematica

Numerator[Convergents[Sqrt[57], 30]] (* Vincenzo Librandi, Oct 25 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 302, 0, 0, 0, 0, 0, -1}, {7, 8, 15, 68, 83, 151, 2197, 2348, 4545, 20528, 25073, 45601}, 30] (* Harvey P. Dale, Jul 22 2016 *)

Crossrefs

Cf. A010510, A041099.

Sequence in context: A066971 A084377 A041675 * A041427 A042755 A093083

Adjacent sequences: A041095 A041096 A041097 * A041099 A041100 A041101

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved