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

0,3

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A041176.

Sequence in context: A248306 A336690 A375790 * A041178 A221201 A119159

Adjacent sequences: A041174 A041175 A041176 * A041178 A041179 A041180

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 12 2013

Status

approved