A041161 Denominators of continued fraction convergents to sqrt(90).

1, 2, 37, 76, 1405, 2886, 53353, 109592, 2026009, 4161610, 76934989, 158031588, 2921503573, 6001038734, 110940200785, 227881440304, 4212806126257, 8653493692818, 159975692596981, 328604878886780

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

Crossrefs

Cf. A041160.

Programs

Magma

I:=[1, 2, 37, 76]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[90],30]] (* Harvey P. Dale, May 20 2013 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 38 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Formula

G.f.: (1 +2*x -x^2)/(x^4 -38*x^2 +1). - Vincenzo Librandi, Dec 12 2013

a(n) = 38*a(n-2) - a(n-4), - Vincenzo Librandi, Dec 12 2013