A041616 Numerators of continued fraction convergents to sqrt(327).

18, 217, 7830, 94177, 3398202, 40872601, 1474811838, 17738614657, 640064939490, 7698517888537, 277786708926822, 3341139025010401, 120558791609301258, 1450046638336625497, 52322237771727819150, 629316899899070455297, 22707730634138264209842

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, 434, 0, -1).

Formula

G.f.: -(x^3-18*x^2-217*x-18)/(x^4-434*x^2+1). - Vincenzo Librandi, Nov 05 2013

a(n) = 434*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[327], 30]] (* or *) CoefficientList[Series[-(x^3 - 18 x^2 - 217 x - 18)/(x^4 - 434 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 05 2013 *)
LinearRecurrence[{0, 434, 0, -1}, {18, 217, 7830, 94177}, 20] (* Harvey P. Dale, Sep 10 2019 *)

Prog

(Magma) I:=[18, 217, 7830, 94177]; [n le 4 select I[n] else 434*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 05 2013

Crossrefs

Cf. A041617.

Sequence in context: A021503 A025470 A046915 * A224296 A019333 A021454

Adjacent sequences: A041613 A041614 A041615 * A041617 A041618 A041619

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 09 2013

Status

approved