A041177 Denominators of continued fraction convergents to sqrt(98).

1, 1, 9, 10, 189, 199, 1781, 1980, 37421, 39401, 352629, 392030, 7409169, 7801199, 69818761, 77619960, 1466978041, 1544598001, 13823762049, 15368360050, 290454242949, 305822602999, 2737035066941, 3042857669940, 57508473125861, 60551330795801, 541919119492269

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, 0, 0, 198, 0, 0, 0, -1).

Crossrefs

Cf. A041176.

Programs

Magma

I:=[1, 1, 9, 10, 189, 199, 1781, 1980]; [n le 8 select I[n] else 198*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[98], 30]] (* or *) CoefficientList[Series[(1 + x + 9 x^2 + 10 x^3 - 9 x^4 + x^5 - x^6)/(1 - 198 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Formula

G.f.: (1 +x +9*x^2 +10*x^3 -9*x^4 +x^5 -x^6)/(1 -198*x^4 +x^8). - Vincenzo Librandi, Dec 12 2013

a(n) = 198*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 12 2013

Extensions

More terms from Vincenzo Librandi, Dec 12 2013