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
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).
Programs
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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 *)
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]