A042778 Numerators of continued fraction convergents to sqrt(920).

30, 91, 5490, 16561, 999150, 3014011, 181839810, 548533441, 33093846270, 99830072251, 6022898181330, 18168524616241, 1096134375155790, 3306571650083611, 199490433380172450, 601777871790600961, 36306162740816230110, 109520266094239291291, 6607522128395173707570

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,182,0,-1).

Formula

G.f.: (30 + 91*x + 30*x^2 - x^3)/(1 - 182*x^2 + x^4). - Vincenzo Librandi, Dec 04 2013, simplified by Colin Barker, Dec 23 2013

a(n) = 33122*a(n-4) - a(n-8) = 182*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013

Mathematica

Numerator[Convergents[Sqrt[920], 30]] (* or *) CoefficientList[Series[(30 + 91 x + 30 x^2 - x^3)/(1 - 182 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)
LinearRecurrence[{0, 182, 0, -1}, {30, 91, 5490, 16561}, 30] (* Harvey P. Dale, Oct 20 2024 *)

Prog

(Magma) I:=[30, 91, 5490, 16561]; [n le 4 select I[n] else 182*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013

Crossrefs

Cf. A042779, A040889.

Sequence in context: A306121 A042774 A042776 * A031212 A165133 A044217

Adjacent sequences: A042775 A042776 A042777 * A042779 A042780 A042781

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 04 2013

Status

approved