A041894 Numerators of continued fraction convergents to sqrt(469).
21, 22, 43, 65, 693, 4223, 42923, 47146, 90069, 137215, 5853099, 5990314, 11843413, 17833727, 190180683, 1158917825, 11779358933, 12938276758, 24717635691, 37655912449, 1606265958549, 1643921870998, 3250187829547, 4894109700545, 52191284834997
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, 0, 0, 0, 0, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[469], 30]] (* Harvey P. Dale, Mar 28 2013 *)
Formula
G.f.: -(x^19 -21*x^18 +22*x^17 -43*x^16 +65*x^15 -693*x^14 +4223*x^13 -42923*x^12 +47146*x^11 -90069*x^10 -137215*x^9 -90069*x^8 -47146*x^7 -42923*x^6 -4223*x^5 -693*x^4 -65*x^3 -43*x^2 -22*x -21) / (x^20 -274430*x^10 +1). - Colin Barker, Nov 26 2013
Extensions
More terms from Colin Barker, Nov 26 2013