A041615 Denominators of continued fraction convergents to sqrt(326).

1, 18, 649, 11700, 421849, 7604982, 274201201, 4943226600, 178230358801, 3213089685018, 115849459019449, 2088503352035100, 75301970132283049, 1357523965733129982, 48946164736524962401, 882388489223182453200, 31814931776771093277601

Offset

0,2

Links

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

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

Formula

G.f.: -(x^2-18*x-1) / (x^4-650*x^2+1). - Colin Barker, Nov 20 2013

a(n) = 650*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[326], 20]] (* Harvey P. Dale, Jul 06 2013 *)
CoefficientList[Series[(1 + 18 x - x^2)/(x^4 - 650 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 18, 649, 11700]; [n le 4 select I[n] else 650*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041614, A040307.

Sequence in context: A322889 A003298 A049869 * A041612 A046674 A073421

Adjacent sequences: A041612 A041613 A041614 * A041616 A041617 A041618

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved