A041080 Numerators of continued fraction convergents to sqrt(47).
6, 7, 41, 48, 617, 665, 3942, 4607, 59226, 63833, 378391, 442224, 5685079, 6127303, 36321594, 42448897, 545708358, 588157255, 3486494633, 4074651888, 52382317289, 56456969177, 334667163174, 391124132351, 5028156751386, 5419280883737, 32124561170071
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,96,0,0,0,-1).
Programs
-
Mathematica
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[47],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*) Numerator[Convergents[Sqrt[47],30]] (* Harvey P. Dale, Oct 15 2013 *)
Formula
G.f.: -(x^7-6*x^6+7*x^5-41*x^4-48*x^3-41*x^2-7*x-6) / (x^8-96*x^4+1). - Colin Barker, Nov 04 2013
Extensions
More terms from Colin Barker, Nov 04 2013