A041614 Numerators of continued fraction convergents to sqrt(326).

18, 325, 11718, 211249, 7616682, 137311525, 4950831582, 89252280001, 3218032911618, 58013844689125, 2091716441720118, 37708909795651249, 1359612469085165082, 24510733353328622725, 883746013188915583182, 15931938970753809120001, 574433548960326043903218

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,650,0,-1).

Formula

G.f.: -(x^3-18*x^2-325*x-18)/(x^4-650*x^2+1). - Vincenzo Librandi, Nov 05 2013

a(n) = 650*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[326], 30]] (*or *) CoefficientList[Series[-(x^3 - 18 x^2 - 325 x - 18)/(x^4 - 650 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 05 2013 *)
LinearRecurrence[{0, 650, 0, -1}, {18, 325, 11718, 211249}, 30] (* Harvey P. Dale, Jan 01 2014 *)

Prog

(Magma) I:=[18, 325, 11718, 211249]; [n le 4 select I[n] else 650*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 05 2013

Crossrefs

Cf. A041615.

Sequence in context: A285875 A223311 A041145 * A222812 A166787 A280806

Adjacent sequences: A041611 A041612 A041613 * A041615 A041616 A041617

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 09 2013

Status

approved