A041756 Numerators of continued fraction convergents to sqrt(398).

19, 20, 379, 399, 15541, 15940, 302461, 318401, 12401699, 12720100, 241363499, 254083599, 9896540261, 10150623860, 192607769741, 202758393601, 7897426726579, 8100185120180, 153700758889819

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,798,0,0,0,-1).

Formula

G.f.: (19 + 20*x + 379*x^2 + 399*x^3 + 379*x^4 - 20*x^5 + 19*x^6 - x^7)/(1 - 798*x^4 + x^8). - Vincenzo Librandi, Nov 08 2013

a(n) = 798*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 08 2013

Mathematica

Numerator[Convergents[Sqrt[398], 30]] (* Harvey P. Dale, Nov 29 2012 *)
CoefficientList[Series[(19 + 20 x + 379 x^2 + 399 x^3 + 379 x^4 - 20 x^5 + 19 x^6 - x^7)/(1 - 798 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 08 2013 *)

Prog

(Magma) I:=[19, 20, 379, 399, 15541, 15940, 302461, 318401]; [n le 8 select I[n] else 798*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 08 2013

Crossrefs

Cf. A041757.

Sequence in context: A041754 A197353 A041179 * A041757 A041758 A042735

Adjacent sequences: A041753 A041754 A041755 * A041757 A041758 A041759

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved