A041187 Denominators of continued fraction convergents to sqrt(104).

1, 5, 101, 510, 10301, 52015, 1050601, 5305020, 107151001, 541060025, 10928351501, 55182817530, 1114584702101, 5628106328035, 113676711262801, 574011662642040, 11593909964103601, 58543561483160045, 1182465139627304501, 5970869259619682550

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,102,0,-1).

Formula

G.f.: (1 + 5*x - x^2)/(1 - 102*x^2 + x^4). - Vincenzo Librandi, Dec 12 2013

a(n) = 102*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[104], 30]] (* or *) CoefficientList[Series[(1 + 5 x - x^2)/(1 - 102 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0, 102, 0, -1}, {1, 5, 101, 510}, 30] (* Harvey P. Dale, Mar 12 2015 *)

Prog

(Magma) I:=[1, 5, 101, 510]; [n le 4 select I[n] else 102*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041186.

Sequence in context: A087456 A081220 A210362 * A266235 A266452 A354332

Adjacent sequences: A041184 A041185 A041186 * A041188 A041189 A041190

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 12 2013

Status

approved