A041133 Denominators of continued fraction convergents to sqrt(75).

1, 1, 2, 3, 50, 53, 103, 156, 2599, 2755, 5354, 8109, 135098, 143207, 278305, 421512, 7022497, 7444009, 14466506, 21910515, 365034746, 386945261, 751980007, 1138925268, 18974784295, 20113709563, 39088493858, 59202203421, 986323748594, 1045525952015

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,52,0,0,0,-1).

Crossrefs

Cf. A041132, A020832, A010153.

Programs

Magma

I:=[1, 1, 2, 3, 50, 53, 103, 156]; [n le 8 select I[n] else 52*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[75], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 3 x^2 + 1)/(x^8 - 52 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,52,0,0,0,-1},{1,1,2,3,50,53,103,156},40] (* Harvey P. Dale, Aug 03 2024 *)

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-52*x^4+1). - Colin Barker, Nov 13 2013

a(n) = 52*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013