A042768 Numerators of continued fraction convergents to sqrt(915).

30, 121, 7290, 29281, 1764150, 7085881, 426917010, 1714753921, 103312152270, 414963363001, 25001113932330, 100419419092321, 6050166259471590, 24301084456978681, 1464115233678192450, 5880762019169748481, 354309836383863101310, 1423120107554622153721

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 242, 0, -1).

Formula

G.f.: (30 +121*x +30*x^2 -x^3)/(1 -242*x^2 +x^4). - Vincenzo Librandi, Dec 04 2013

a(n) = 242*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[915], 30]] (* or *) CoefficientList[Series[(30 + 121 x + 30 x^2 - x^3)/(1 - 242 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

Prog

(Magma) I:=[30, 121, 7290, 29281]; [n le 4 select I[n] else 242*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013

Crossrefs

Cf. A042769.

Sequence in context: A042764 A219223 A042766 * A122137 A003901 A010744

Adjacent sequences: A042765 A042766 A042767 * A042769 A042770 A042771

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 04 2013

Status

approved