A041130 Numerators of continued fraction convergents to sqrt(74).
8, 9, 17, 26, 43, 714, 757, 1471, 2228, 3699, 61412, 65111, 126523, 191634, 318157, 5282146, 5600303, 10882449, 16482752, 27365201, 454325968, 481691169, 936017137, 1417708306, 2353725443, 39077315394, 41431040837, 80508356231, 121939397068, 202447753299
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,86,0,0,0,0,1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[74], 30]] (* Vincenzo Librandi, Oct 29 2013 *) LinearRecurrence[{0,0,0,0,86,0,0,0,0,1},{8,9,17,26,43,714,757,1471,2228,3699},40] (* Harvey P. Dale, Sep 18 2024 *)
Formula
G.f.: -(x^9-8*x^8+9*x^7-17*x^6+26*x^5+43*x^4+26*x^3+17*x^2+9*x+8) / (x^10+86*x^5-1). - Colin Barker, Nov 05 2013
Extensions
More terms from Colin Barker, Nov 05 2013