A042758 Numerators of continued fraction convergents to sqrt(910).

30, 181, 10890, 65521, 3942150, 23718421, 1427047410, 8586002881, 516587220270, 3108109324501, 187003146690330, 1125126989466481, 67694622514679190, 407292862077541621, 24505266347167176450, 147438890945080600321, 8870838723052003195710

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,362,0,-1).

Formula

G.f.: (30 +181*x +30*x^2 -x^3)/(1 -362*x^2 +x^4). - Vincenzo Librandi, Dec 04 2013

a(n) = 362*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[910], 30]] (* or *) CoefficientList[Series[(30 + 181 x + 30 x^2 - x^3)/(1 - 362 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

Prog

(Magma) I:=[30, 181, 10890, 65521]; [n le 4 select I[n] else 362*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013

Crossrefs

Cf. A042759.

Sequence in context: A042756 A281999 A156318 * A071311 A337494 A265037

Adjacent sequences: A042755 A042756 A042757 * A042759 A042760 A042761

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 04 2013

Status

approved