A041766 Numerators of continued fraction convergents to sqrt(404).

20, 201, 8060, 80801, 3240100, 32481801, 1302512140, 13057603201, 523606640180, 5249124005001, 210488566840220, 2110134792407201, 84615880263128260, 848268937423689801, 34015373377210720300, 341002002709530892801, 13674095481758446432340

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,402,0,-1).

Formula

G.f.: (20 + 201*x + 20*x^2 - x^3)/(1 - 402*x^2 + x^4). - Vincenzo Librandi, Nov 07 2013

a(n) = 402*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 07 2013

Mathematica

Numerator[Convergents[Sqrt[404], 30]] (* or *) CoefficientList[Series[(20 + 201 x + 20 x^2 - x^3)/(1 - 402 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 07 2013 *)
LinearRecurrence[{0, 402, 0, -1}, {20, 201, 8060, 80801}, 20] (* Harvey P. Dale, Oct 27 2018 *)

Prog

(Magma) I:=[20, 201, 8060, 80801]; [n le 4 select I[n] else 402*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 07 2013

Crossrefs

Cf. A041767.

Sequence in context: A120787 A223753 A099197 * A121088 A302838 A302921

Adjacent sequences: A041763 A041764 A041765 * A041767 A041768 A041769

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Status

approved