A041275 Denominators of continued fraction convergents to sqrt(150).

1, 4, 97, 392, 9505, 38412, 931393, 3763984, 91267009, 368832020, 8943235489, 36141773976, 876345810913, 3541525017628, 85872946233985, 347033309953568, 8414672385119617, 34005722850432036, 824552020795488481

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 (0,98,0,-1).

Crossrefs

Cf. A041274.

Programs

Magma

I:=[1,4,97,392]; [n le 4 select I[n] else 98*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[150], 30]] (* or *) CoefficientList[Series[(1 + 4 x - x^2)/(x^4 - 98 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

Formula

G.f.: (1 +4*x -x^2)/(x^4 -98*x^2 +1). - Vincenzo Librandi, Dec 14 2013

a(n) = 98*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 14 2013